Giáo án Toán song ngữ lớp 11 chương 3

Date of preparation:
Date of teaching:

CHAPTER III

VECTORS IN SPACE. PERPENDICULAR RELATIONSHIPS IN SPACE
Period 28.

Problem 1. VECTORS IN SPACE

I. Objectives:
Through lessons students should:
1. Knowledge:
- Boxy communist rule for vectors in space;
- Concept and conditions of the three vectors coplanar in space.
2. Skills:
- Transportation Permitted use addition, subtraction vectors, the vector with a number, the dot product of two
vectors, the equality of the two vectors in space to solve exercises.
- Discriminatory manner not consider the coplanar or coplanar of three vectors in space.
3. Thinking: + Develop abstract thinking, spatial imagination
+ Know observation and accurate judgment
4. Attitude: Be careful, accurate, seriously, very actively working
II. Prepare:
Teacher: Lesson plans, handout, ..
Student: Write articles before class, answer the questions in the activity.
III. Method:
- Prompt open, oral, group activities overlap.
III. Progress lesson:
1) Stable layers, introducing: Divide the class into six groups
2) New lesson:
TEACHER ACTIVITIES - STUDENT ACTIVITIES

CONTENT
Activity 1: Learn about
I.Definition of and operations on
definitions and calculations of
-Student stated definition ...
vectors in space:
vectors in space.
-Student discussion groups to 1) Definition: (See book)
Active ingredient 1:
find solutions and to appoint
Activities 1: book
-Student: teacher called a
their representatives on the
A
stated definition of vectors in
board to present the answer
space.
(girls love)
-Teacher for student discussion -Student comments, additions
groups to find solutions 1 and 2 and repair records.
operations.
-Student exchange and draw
-Teacher illustrations on the
results: ...
board ...
-Student represents the group
D
B
called on the board to present
the answer.

Call student comment and
C
supplement (if necessary).
Activities 2:

-Teachers comment stating the
correct answer (if the student
does not present the correct
answer)


B

C

A

D

C'

B'

Activity component 2:
Addition and subtraction
vectors in space:
-Teacher: Addition and
subtraction of two vectors in
space is defined the same as
addition and subtraction of two

vectors in space phang.Vecto
surface properties such as in the
plane.
-The teacher called the student
stating the properties of vectors
in the plane, such as 3-point
rule, the rule of the
parallelogram, ...
-Teachers mentioned example 1
(textbooks) and the student
discussion groups to find a
solution.
-Call the student representative
on the board to present the
answer.
-Teachers nominate students to
comment and supplement (if
necessary)
-The teacher comments and
supplement stating the correct
answer (if the student is not
present right answer)
Activity 3 components:
-Teachers give students the
discussion group to find
solutions operate 3 in the
textbook.
-Students to review and
supplement (if necessary)
-The teacher comments and

supplement stating the correct
answer (if the student is not
present right answer)
Active ingredient 4: Rules box:
-Teachers draw up tables and
analysis proves to come to rule
the box by offering the

-Students tuned to acquire
knowledge ...

A'

D'

-Students think and recall the
properties of vectors in plane
geometry ...
-Students view and discuss
problems to find the answer ...
-The student representative on
the board hanging side table
and explain the results.
-Students comments,
additions and repair records.
-Students discuss and draw
results:
...

Activities 3: Given cube

ABCD.EFGH. Perform the the
following operations:
uuu
r uuur uuu
r uuur
a) AB + CD + EF + GH
uuu
r uuuv
b) BE − CH
*Cube
rule:
uuuu
r uuu
r uuur uuuur
AC ' = AB + AD + AA '
B

C

A

-Student group discussions to
find a solution and to send
representatives to the board
presented a solution (with an
explanation).
-Student comments, additions
and repair records.
-Student exchanges to draw
results:

....
ABC'D 'parallelogram
...

D

C'

B'

A'

D'


following problems:
ABCD.A'B'C'D box for
'demonstrating
uuu
r uuur uuuurthat:
uuuu
r
AB + AD + AA ' = AC '
-Teacher for student discussion
groups to find a solution and
called student representatives
on the board presented a
solution.
-Call student comment and
supplement (if necessary)

-Teacher comments, additions
and stating the correct answer
(if not presented properly
student solution)
Activity 2: Multiplication
3. Scalar multiple of a vector:
vectors with a number:
Example 2: (see textbook)
Active ingredient 1:
-Students view content groups
-Teacher: In the space of an
2 and discuss examples to find
area with a number of similar
the solution to send
vectors as defined in the plane.
representatives to the board
A
-Teachers give students a view
and presented (with
contents examples 2 and
interpretation)
discussion groups to find a
--Students comments,
solution.
additions and repair records.
M
-Call the student representative -Exchange students to draw
on the board to present the
results:
answer.

...
-Students to review and
D
B
supplement (if necessary).
-Teacher comments, additions
G
N
and repairs recorded (if the
student does not present the
correct answer)
C
Activity 2 components:
-Teachers give students the
-Students talk to find a
discussion group to find
solution and to send
solutions working example 4 in representatives to the board
textbooks and student
presented a solution (with an
representatives called on the
explanation)
board to present the answer.
-Students comments,
-Call students additional
additions and repair records.
comments (if necessary)
-Students discuss and draw
-The teacher comments and
results:

supplement stating the correct
...
answer (if the student is not
present right answer)
3: strengthened and guided learning at home:
*Consolidate:
-If The concept of vectors in space, the properties of the vector in space, with an area of some vectors.
Its gauge: For HS discussion groups to find answers exercises 1 and 2 textbooks and student representative on
the board called to present a solution (with an explanation).


* Guides at home:
-Review And follow the textbook theory.
-Prepare Before the rest, do more exercises 3.4 and 5 textbooks 91. Page 92.
------------------------------ ************** -----------------------Date of preparation:
Date of teaching:
Period 29.

VECTORS IN SPACE.

I. Objectives:
Through lessons students should:
1. Knowledge:
Concept and conditions of the three vectors coplanar in space.
2. Skills:
-Transportation Permitted use addition, subtraction vectors, the vector with a number, the dot product of two
vectors, the equality of the two vectors in space to solve exercises.
Discriminatory manner not consider the coplanar or coplanar of three vectors in space.
3. Thinking: + Develop abstract thinking, spatial imagination
+ Know observation and accurate judgment

4. Attitude: Be careful, accurate, seriously, very actively working
II. Prepare:
Teachers: Lesson Plans, textbooks,
Students: Write articles before class, answer the questions in the activity.
III. Method:
- Prompt open, oral, group activities overlap.
III. Progress lesson:
* Stable layers, introducing: Divide the class into six groups
*New lesson:
TEACHER ACTIVITIES - STUDENT ACTIVITIES
CONTENT
Activity 1: The concept of the
II. Coplanar conditions of three
three vectors coplanar in space:
vectors:
Active ingredient 1:
1) Concept of the coplanarity of
-The teacher called the students
three vectors in space:
to repeat the same concept 2
-Students repeat the same
vectors.
concepts 2 vector ...
-Teacher drawing and vector
-Students tuned on the table ...
analysis showed 3 coplanar and
non-coplanar and ask questions.
So in the space when the three
-Students think about and
O

A
vectors coplanar?
answer:
B
-Three vectors coplanar when
their prices along parallel to a
-The teacher called a student
plane.
C
referred to the definition of the
-Students mentioned in the
2) Definition:
three vectors coplanar, drawing textbook definition.
* Figure 3.6 book.
teacher and write a summary on
In space three vectors are called
the table (or can hook the side
coplanar if their bases are parallel
panel)
to the same plane.
Activity component 2:

Example


Example of application:
-Teachers give students the
class content working example
5 in textbooks and student
discussion groups to find a

solution, called the student
representative on the board of
the group presented a solution.
-Students to review and
supplement (if necessary).
-The teacher comments and
supplement stating the correct
answer (if the student is not
present right answer)
Activity 2: Requirement 3
coplanar vectors:
Active ingredient 1:
-The teacher called a student
mentioned content theorem 1.
-Teachers drawing, analysis and
suggestions (Use rules
parallelogram).
-Teachers give students
brainstorm to find solutions and
student representatives called
on the board to present the
answer.
-Students to review and
supplement (if necessary).
-Teacher comments, additions
and raised right lf (if the student
does not present the correct
answer)
Activity 2 components:
-Teachers give students the

discussion group to find
solutions working example 6
and referred the student
representative on the board the
group presented a solution.
-Students to review and
supplement (if necessary).

-Teachers comment stating the
correct answer (if the student

-Student discussion groups to
find a solution on the board
and representatives of the
presentation (with
interpretation)
-Students comments,
additions and repair records.
Exchange students to
uurdraw
uuur
results: the vectors IK , ED
priced parallel to the
uuu
rplane
(AFC) and vector AF located
in the plane cost (AFC) to
three coplanar vectors.

Activities 5: (Book)

D

K
A

I

B

H
G

E

-Students mentioned theorem
1 in textbooks and drawings
CGU tuned to discuss in
groups seek to prove theorem
1 ...
-The student representative on
the board the group presented
a solution (with an
explanation).
-Students comments,
additions and repair records.
Exchange students to draw
results:
...

C

F

3) Conditions for three vectors to
be coplanar:
Theorem 1: (See book)

-Students in group discussions
to find a solution and to send
Example activities 6: book
representatives to the board
presented a solution (with an
explanation).
-Students comments,
additions and repair records.
Exchange students to draw
results;
vector
Construction
r
r
2 a and vect¬ -b . According
off of two vectors subtraction
we find vectors
r
r r
r
r
c = 2a − b = 2 a + − b . If

r
r r
c = 2a − b should follow the
r r r
three vectors theorem 1 a, b, c Example Activities 7: Book
coplanar

( )


does not correct answers
presented)
Activity 3 components:
Similarly teachers for student
discussion groups to find a
solution by working example 7
and called the student
representative on the board to
present the answer.
Students to review and
supplement (if necessary).

Students discuss in groups to
find solutions and to appoint
their representatives on the
board to present the answer
(with an explanation)
Students comments, additions
and repair records.
Exchange students to draw

results:
r
r
r r
We have: ma + nb + pc = 0
and suppose p ≠ 0 . Then we
can write:
r
mr nr
c = − a− b
p
p
Dress …

Teachers comment stating the
correct answer (if the student
does not present the correct
answer)
3: strengthened and guided learning at home:
*Consolidate:
- The conditions of the three vectors coplanar.
SOAP provides the exercises use:
uuu
r uuur uuur
uuur
1) For the tetrahedron ABCD, called G is central triangle BCD. Prove that: AB + AC + AD = 3 AG
uuur uuur uu
r
2) Given the tetrahedron ABCD. Call I and J respectively midpoint of AB, CD. Prove that AC, BD, IJ is the
vectors coplanar.

* Guides at home:
-See And follow the textbook theory.
-Make More exercises 1, 2, 3, 4.5, 7 and 10 in the textbook.
-----------------------------------------------------------------------

Date of preparation:


Date of teaching:

Period 30: Practice
I. Objectives:
Through the lesson students should:
1. Knowledge:
Concept and conditions of the three vectors coplanar in space.
2. Skills:
-Transportation Permitted use addition, subtraction vectors, the vector with a number, the dot product of two
vectors, the equality of the two vectors in space to solve exercises.
Discriminatory manner not consider the coplanar or coplanar of three vectors in space.
3. Thinking: + Develop abstract thinking, spatial imagination
+ Know observation and accurate judgment
4. Attitude: Be careful, accurate, seriously, very actively working
II. Prepare:
Teacher: Lesson plans, textbooks, teacher books, reference books
Students: Write articles before class, answer the questions in the activity.
III. Method:
- Prompt open, oral, group activities overlap.
III. Progress lesson:
* Stable layers, introducing: Divide the class into six groups
*New lesson:

TEACHER ACTIVITIES - STUDENT ACTIVITIES
CONTENT
Problem 1- 7
Activity 1: Provide textbook Students on the board the
textbook exercises
exercises.
Problem: 10
Other students answer your
comment.

Activity 2: The teacher asks
students to comment.
3: Strengthen and direct them at home:
*Consolidate:
-Elevate The conditions of the three vectors coplanar.
SOAP provides the exercises use:
1) For the tetrahedron ABCD, called G is central triangle BCD. Prove that:
2) Given the tetrahedron ABCD. Call I and J respectively midpoint of AB, CD. Prove that is co-planar vectors.
* Guides at home:
-See And learning according to textbook theory.


Date of preparation:
Date of teaching:
Period 31. Problem 2. TWO PERPENDICULAR LINES
I. Objectives:
Through the lesson students should:
1. Knowledge:
-Only the concept of the straight line vector;
-Concept angle between two lines;

2. Skills:
-Identify Be the only vector of the line, the angle between two lines.
Discriminant prove two perpendicular lines.
3. Thinking: + Develop abstract thinking, spatial imagination
+ Know observation and accurate judgment
4. Attitude: Be careful, precise, serious, active
II. Prepare:
Teachers: Lesson Plans, handout, ..
Students: Write articles before class, answer the questions in the activity.
III. Method:
- Prompt open, oral, group activities overlap.
III. Progress lesson:
* Stable layers, introducing: Divide the class into six groups
*New lesson:
TEACHER ACTIVITIES - STUDENT ACTIVITIES
CONTENT
Activity 1:
I. DOT PRODUCT OF TWO
Active ingredient 1: Learn
SPATIAL VECTORS:
about the angle between two
1) An angle between two
vectors in space:
spatial vectors:
The teacher called a student
Students mentioned in the textbook
Definition: (book)
mentioned in the textbook
definition
r

definition, teachers hang the
v
side panel with figures 3:11 (as Tuned on the table to acquire
in textbooks on the board) and
knowledge ...
B
analyze written notation ...
A
C
r
u
·
Angle BAC
is angle between
r
r
two vector v and u in space
·
0 0 ≤ BAC
≤ 180 0 , denote :

(r r

( u, v )
Activity component 2:
Example of application:
Teachers give students the
discussion group to find
solutions working example 1
and called the student

representative on the board
presentation team explains.

Student discussion groups to find
solutions and to appoint their
representatives on the board
presented a solution (with an
explanation)
Students comments, additions and
repair records.

)

Exampe activities 1: (book)


Teachers nominate students to
comment and supplement (if
necessary)

The teacher comments and
supplement stating the correct
answer (if the student is not
present right answer)

Active ingredient 3: The inner
product of two vectors:
-The teacher called a student to
repeat the scalar concept of two
vectors in the plane geometry

and formulas on the blackboard
to record the dot product of two
vectors.
-Teacher: In the geometry of
space, scalar product of two
vectors is defined entirely
similar.
-The teacher called a student
referred to the definition of the
scalar product of two vectors in
space.
Active ingredient 4: examples
of application:
-Teachers give students the
discussion group to find
solutions working example 2
and referred students to the
board represents the solution
presented.
-Students to review and
supplement (if necessary)
-The teacher comments and
supplement stating the correct
answer (if the student is not
present right answer)

Activity 2: learn about the
only vector of the line:
Active ingredient 1:

A

Exchange students to draw results:
With tetrahedron ABCD because H
is the midpoint of AB, so we have:
uuu
r uuu
r
AB, BC = 120 0
uuur uuur
CH , AC = 150 0

(
(

)

)

Students recall the concept of the
scalar product of two vectors in the
plane geometry.

H

K
D
B

C

2) Dot product of two
spatial vectors:
* Definition: (See book)

r rr r
u ≠ 0, v ≠ 0, we have :
rr r r
rr
u.v = u v .cos u, v

Students referred to the concept of
the scalar product of two vectors in
space (in textbooks)

( )

r rr r
if u = 0, v = 0, then by
rr
convention : u.v = 0

Student discussion groups to find
solutions and to appoint their
representatives on the board
presented a solution (with an
explanation)

D

C

A
B

Students comments, additions and
repair records.
Exchange students to draw results:
uuur uuu
r uuur uuur
AC ' = AB + AD + AA '
uuur uuur uuu
r
uuu
r uuur
BD = AD − AB = − AB + AD
uuur uuur
uuur uuur
AC '.BD
cos AC ', BD = uuur uuur
AC ' BD
uuur uuur uuur uuur uuur uuur uuur
AC '. BD = ( AB + AD + AA ')( AD − AB)
uuur uuur uuur2 uuur2 uuur uuur
= AB. AD − AB + AD − AD. AB +
uuur uuur uuur uuur
uuur2 uuur2
AA '. AD − AA '. AB = − AB + AB
uuur uuur
So cos AC ', BD = 0

uuur uuur
Therefore: AC' ⊥ BD

(

(

C'

D'

A'

B'

)

(

)

(

) (

)

)

(

)

II. Direction vectors of a line
1) Definition: (book)
Students mentioned in the textbook


The teacher called a student
referred to the definition of the
only vector of a line.
The teacher poses questions:
If only the vectors of the vector
k d line with vector k 0 Is the
line d only way not? Why?
A straight line d in space is
completely determined when?
Two lines d and d 'parallel
when?
Teachers ask students in the
class textbook reviewers.

definition.
d
Students brainstorm answers and
explanations ...

r
a

r r
a ≠ 0 is called direction
vectors of a line d
2) Remarks:
(book)
r
a) If a is yhe direction
vector ofrthe line d, then
vector k a with k ≠ 0 is also a
direction vector of line d.
b)…

3: strengthened and guided learning at home:
*Consolidate:
-Nhac The concept of angle between two vectors in space and only the concept vectors.
Its gauge: Good exercises 1 and 2 textbooks
Teachers give students the discussion groups to find a solution and called students to the board represents
the solution presented.
The teacher comments and supplement stating the correct answer (if the student is not present right
answer)
* Guides at home:
-Review And learning according to textbook theory.
-Make The exercises 3, 4, 5, 6 in the textbook pages 97, 98.
-----------------------------------------------------------------------


Date of preparation:
Date of teaching:

Period 32: EXERCISE

I. Objectives:
Through the lesson students should:
1. Knowledge:
Concept and conditions for the two perpendicular lines.
2. Skills:
-Identify Be the only vector of the line, the angle between two lines.
Discriminant prove two perpendicular lines.
3. Thinking: + Develop abstract thinking, spatial imagination
+ Know observation and accurate judgment
4. Attitude: Be careful, precise, serious, active
II. Prepare:
Teachers: Lesson Plans, handout, ..
Students: Write articles before class, answer the questions in the activity.
III. Method:
- Prompt open, oral, group activities overlap.
III. Progress lesson:
* Stable layers, introducing: Divide the class into six groups
* Check Oldest: Combined with the active control group.
*New lesson:
TEACHER ACTIVITIES - STUDENT ACTIVITIES
CONTENT
Activity 1: Learn about the
III. An angle between two lines in
angle between two lines in
space:
space:
1) Definition: (book)
Active ingredient 1:
The angle between two lines a and

-The teacher called a student to Students thinking reiterated
b in space is the angle between line
repeat the definition angle
defined angle between two
a’ and line b’ all passing through a
between two straight lines in the straight lines in the plane.
point and parallel to line a and line
plane.
The angle between the
b, respectively.
The angle between the straight
straight line measurement in
line measurement in place?
paragraph
-Teacher: Based on the
a
definition of the angle between
two straight lines in the plane
b
they built defines the angle
a’
between two lines in space. So
Answer students think ...
b’
according to them the angle
between two lines in space is
how the corner?
-The teacher called a student
Students referred to the
referred to the definition of the

definition of the angle
angle between the straight line
between the straight line in
in space.
space ...
-Teachers draw pictures and
instructions on how to draw the
lines in the corners of the space.
-Teachers ask questions:
To determine the angle between Answer students think ...
two lines a and b in space like
we do?
Example activities 3: (book)


r
If u is the only vector of a
r
straight line and v is the only
r
vector of the straight line b ( u ,
r
v ) Is the angle between two
lines a and b are not? Why?
When is the angle between the
straight line in space by
00?
Teachers remarked in textbooks
and ask students whether in
textbooks.

Activity component 2: Exercise
of application:
Teachers give students the
discussion groups to find a
solution examples 3 and called
school activities sinhv results
represent the fastest team on the
board presentation.
Students to review and
supplement (if necessary)
The teacher comments and
supplement stating the correct
answer (if the student is not
present right answer)
Activity 2: Learn about two
perpendicular lines:
Active ingredient 1:
Teacher: In the plane, two
perpendicular lines when?
The definition of two
perpendicular lines in space
similar in the plane.
The teacher called a student
mentioned in the textbook
definition.
Teachers raised questions
system:
rr
- If u, v respectively indicate
the vectors of two lines a and

r rb
and if a ⊥ b then 2 vector u, v
What relationship have?
- For a // b if there is a straight
line so that c ⊥ a how it
compared with b?
-If Two straight lines
perpendicular to each other in
space have confirmed whether it
intersect it?
Activity component 2:
Exercise of application:
-Teachers assign tasks to

D

C

A
B

-Students tuned on the table
to acquire knowledge.
-Student discussion groups to
find solutions and to appoint
their representatives on the
board presentation (with
interpretation)
-Students comments,
additions and repair records.

Exchange students to draw
results:
· , B ' C ' = 90 0 ; (·AC, B ' C ' ) = 450
AB

(

C'

D'

A'

B'

)

(·A ' C ', B ' C ) = 600
-Students tuned to acquire
knowledge ...

Answer students think ...

IV. Two perpendicular lines:
1) Definition: (book)
Two lines are said to be
perpendicular if the angle between
them equals 90 degree.
Two lines a and b perpendicular to
each other are denoted by a ⊥ b

a

Students mentioned in the
textbook definition.
Answer students think ...
rr
u.v = 0
a / / b
⇒c⊥b

c ⊥ a
Not confirmed, as can two
straight lines that cross each
other.
Student discussion groups to
find solutions and to appoint
their representatives on the

O

b

b’
Remarks: (book)
Example activities 4: (book)


students in discussion groups to
find solutions working example
4 and 5.

-Call the student representative
on the board to present the
answer.
-Students to review and
supplement (if necessary)
-The teacher comments and
supplement stating the correct
answer (if the student is not
present right answer)

board presentation (with
interpretation)

D

C

A

Students comments, additions
and repair records.
Exchange students to draw
results: ...

B

C'

D'

A'

B'

Example activities 5: (book)
V. Exercise
3: strengthened and guided learning at home:
*Consolidate:
Students to repeat the definitions: The angle between two lines, two perpendicular lines, condition of two
perpendicular lines.
* Application: Solve exercise 5, 7 and 8 textbooks.
Teachers assign tasks to groups and student representatives called on the board to present the answer.
The teacher comments and supplement stating the correct answer (if the student is not present right answer)
* Guides at home:
-Review And learning according to textbook theory.
Further cooling the remaining exercises in the textbook pages 97 and 98.

Date of preparation:
Date of teaching:


Period 33. A LINE PERPENDICULAR TO A PLANE
I. Objectives:
Through the lesson students should:
1. Knowledge:
Discriminant defined and conditions for the straight line perpendicular to the mp;
Perpendicular projection concept;
Plane straightforward concept of a line.
2. Skills:
Discriminant demonstrating a straight line perpendicular to a mp, a straight line perpendicular to a line ;.

-Identify Are vectors of a plane.
- Development of abstract thinking, spatial imagination
- Determine the perpendicular projection of a point, a line, a triangle.
Using his first pitch three perpendicular theorem.
-Identify The angle between the straight line and mp.
Discriminant consider the relationship between the parallelism and right angles of lines and mp.
3. Thinking:
+ To develop abstract thinking, spatial imagination.
+ Know observation and accurate judgment.
4. Attitude: Be careful, precise, serious, active.
II. Prepare:
Teachers: Lesson Plans, handout, ..
Students: Write articles before class, answer the questions in the activity.
III. Method:
- Prompt open, oral, group activities overlap.
III. Progress lesson:
* Stable layers, introducing: Divide the class into six groups
* Check Oldest: Combined with the active control group.
*New lesson:
TEACHER ACTIVITIES - STUDENT ACTIVITIES
CONTENT
Activity 1:
I. Definition: (book)
Active ingredient 1: Learn
The line d is said to be
about defining line
perpendicular to plane ( α ) if line d
perpendicular to the mp.
is perpendicular to every line a in
Drawing teachers and students Students mentioned in the

plane ( α )
called a stated definition,
textbook definition
teachers notation.
Students tuned on the table to
acquire knowledge.

Denot by: d ⊥ ( α )

d

a
α

The teacher called the student a
theorem mentioned in
textbooks, teacher to student
discussion groups to find ways

-Students mentioned content
theorem, discussed in groups
to find proof. Appoint
representatives to the board

II. Condition for a line to be
perpendicular to a plane:
Theorem: (book)


to prove theorems.

The teacher called the student
representative on the board to
present the answer.
Students to review and
supplement (if necessary)
Teacher comment, stating
additional evidence (if students
are not presented properly).
From theorem we have the
following consequences:
Teachers stated content in
textbooks consequences.

presented to prove (with
interpretation)
-Students comments,
additions and repair records.

-Students tuned on the table ...
Học sinh suy nghĩ trả lời câu
hỏi của hoạt động 1 và 2.
-Want proof perpendicular
line d with an mp, we
demonstrated perpendicular
line d with two straight lines
which intersect in mp.
...
-Student discussion groups to
Activity component 2:
find solutions and to appoint

Example of application:
their representatives on the
-Teachers mentioned examples board presentation (with
and student discussion groups to interpretation)
find a solution. Call the student -Students comments,
representative on the board to
additions and repair records.
present the answer.
Exchange students to draw
-Students to review and
results: ...
supplement (if necessary).
-Teachers comment stating the
correct answer (if the student
does not present the correct
answer).
Activity 2: Learn about
nature:
Students referred to turn the
Active ingredient 1:
properties and tuned on the
-Teachers nominate students
table to acquire knowledge ...
mentioned in turn the properties
1 and 2 in the textbook
-Teachers draw and analyze ...
Student discussion groups to
Activity component 2: Exercise find solutions and to appoint
apply
their representatives on the

-The teacher mentioned
board presentation (with an
problems exercises (or
explanation).
academic report card)
Students comments, additions
-The teacher asks students to
and repair records.
discussion groups to find a
Exchange students to draw
solution and called on the board results: ...
representing the students
presented.
-Teachers nominate students to
comment and supplement (if
necessary)
-Teacher comment, stating the
correct answer (if the student is
not present right answer)
3: strengthened and guided learning at home:
- Method to prove the apparently vertically hung with mp;

Corollary: (book)
Example activities 1: (book)
Example activities 2: (book)

Problem: Given pyramid S.ABCD
whose base is trapezium ABCD
with right angle at A and B;
SA ⊥ ( ABCD )

a) Prove: BC ⊥ ( SAB )
b) In the triangle SAB, calling H is
the altitude food draw from A.
Prove that: SH ⊥ ( SBC ) .

III. Properties:
Property 1: (book)
Bisecting plane of line segment:
(book)
Property 2: (book)
Problem: Given pyramid S.ABCD
whose base ABCD is square SA
⊥ ( ABCD ) , O is intersection of
two diagonal lines AC and BD of
square ABCD.
a) Prove that: BD ⊥ ( SAC ) ;
b) Prove the triangles SBC, SCD
are right triangles.
c) Determining bisecting plane of
line segment SC.


- The properties;
-Review Solved exercises;
-See And canned the rest in textbooks.
-Make Exercises 1, 2, 3 and 4 Page 105 textbooks.
-----------------------------------------------------------------------


Date of preparation:

Date of teaching:
Period 34. A LINE PERPENDICULAR TO A PLANE
I. Preparation:
Teachers: Lesson Plans,
Students: Write articles before class, answer the questions in the activity.
II. Method:
- Prompt open, oral, group activities overlap.
III. Progress lesson:
* Stable layers, introducing: Divide the class into six groups
* Check Oldest: Combined with the active control group.
*New lesson:
TEACHER ACTIVITIES - STUDENT ACTIVITIES
CONTENT
Activity 1: Learn about the
IV. Relations between parallel
nature of the relationship
relationships and perpendicular
between the parallel and parallel
ralationships of lines and planes.
relationship of line and plane:
Property 1: (book)
Active ingredient 1:
Students tuned to acquire
 a / / b
a) 
⇒ (α) ⊥ b
Teacher drawing and analyzing
knowledge ...
α) ⊥ a
(



the properties leading to contact
between parallel relations and
 a, b : ph©n biÖt

relations of straight lines and right
b
)
⇒ a / /b
a ⊥ ( α )
angles mp.

b ⊥ ( α )

Activity component 2: Example
of application:
Teachers mentioned examples and
student discussion groups to find a
solution.
Example: For S.ABCD bottomed
pyramid ABCD is rectangular and
SA ⊥ ( ABCD ) .
a) Prove: BC ⊥ ( SAB ) and from

that deduced AD ⊥ ( SAB ) .
b) AH is called high street triangle
SAB. Prove: AH ⊥ SB

Activity 2: Learn about the

perpendicular projection and
three perpendicular theorem.
Active ingredient 1:
Drawing teacher and brought him
to the concept leads perpendicular
projection.

figure: 3.22 in book.
Property 2: (book)
Student discussion groups to
find solutions and to appoint a) ( α ) / / ( β ) ⇒ a ⊥ β
( )

their representatives on the
a ⊥ ( α )
board presentation (with
( α ) , ( β ) : distinction
interpretation)

Students comments,
b) ( α ) ⊥ a
⇒ (α) / /( β )
additions and repair records.

( β ) ⊥ a
Student exchange groups to Figure: 3.23 in book.
Property 3: (book)
draw the results: ...
 a / / ( α )
a) 

⇒b⊥a
b
⊥
α
(
)

a ⊄ ( α )

b)  a ⊥ b ⇒ a / / ( α )
 α ⊥b
( )

Students tuned to acquire
knowledge ...

Figure 3.24 in book
V. Perpendicular projections and
theorem of three perpendiculars:
1) Perpendicular projections:
(book)
Given d ⊥ ( α ) , parallel
projections follow in the direction
d is called perpendicular


projections in the plane ( α ) .
Teachers give students the
remarks in textbooks.
Activity component 2: Learn

about three perpendicular
theorem:
Teachers just mentioned and just
illustrations of three perpendicular
theorem.
Instructors demonstrate: a ⊥ b’
⇒ a ⊥ ( b, b ' ) ⇒ a ⊥ b
…

Activity 3 components:
Similar activity sectors 2, teachers
drawing and analysis mentioned
definition of the angle between the
straight lines and planes.
Teachers analyze and solve sample
exercises 2 (or a similar exercise)
textbooks.

A

Students see comments at
textbooks ...

B

A'

Students tuned on the table
to acquire knowledge ...

d

B'

*Remarks: (See book)

2) Theorem of three
Students tuned guidance and perpendiculars: (book)
thoughts in discussion
Figure 3.27 in book
groups to prove theorems ...
B
b
Students tuned to acquire
A
knowledge: On the angle
between the straight lines
and planes ...
Students tuned solution ...

b'
A’

a

B’

3) Angle between a line and a
plane:
Definition: (book)

3: strengthened and guided learning at home:
*Consolidate:
Students reiterated the call of the nature of the relationship between relational and relational parallel straight
lines and right angles of the plane, perpendicular projection, theorems three perpendicular and angle between the
straight lines and planes.
Collective application's problem: Solving episode 6 105 pages of textbooks.
* Guides at home:
-Review And learning according to textbook theory.
-Make More exercises 7 and 8 105 pages of textbooks.

Date of preparation:
Date of teaching:


Period 35: PRACTICE
I. Preparation:
Teachers: Lesson Plans,
Students: Write articles before class, answer the questions in the activity.
II. Method:
- Prompt open, oral, group activities overlap.
III. Progress lesson:
* Stable layers, introducing:
*Check Oldest:
Operates 1: Check the lesson your old
TEACHER ACTIVITIES - STUDENT ACTIVITIES
-How Prove plane perpendicular
lines?
Episode 1's problem / Textbooks /
104?

-up Answer sheet
-All Remaining students replied in
sketchbook
-Comment

CONTENT
Problem 1/ book/ 104 :
a) T
b) F
c) F
d) F

Activity 2: Exercise 2 / textbooks / 104
Episode 2's problem / textbooks /
104?
- How to prove the plane
perpendicular lines?

 BC ⊥ AI
⇒?
 BD ⊥ DI

-

 BC ⊥ ( ADI )
⇒?
-
 BD ⊥ ( ADI )
-Maø DI ⊥ AH ⇒ ?

-Reply
-ERU slant award
-Comment
* Edit perfection
-Burn receive knowledge
- BC ⊥ ( ADI )
- BC ⊥ AH

Problem 2/ book/ 104 :
A

I
B

C
H

- AH ⊥ ( BCD )
D

Activity 3: Exercise 3 / textbooks / 63
- Exercise 3 / textbooks / 104?
- How to prove the plane
perpendicular lines?

 SO ⊥ AC
⇒?
 SO ⊥ BD
 AC ⊥ BD

 BD ⊥ SO
⇒ ?,
⇒?
-
 AC ⊥ SO
 BD ⊥ AC
-

- Reply
-ERU slant award
-Comment
* Edit perfection
-Burn receive knowledge

Problem 3/ book/ 104
S

- SO ⊥ ( ABCD )

D

- AC ⊥ ( SBD ) , BD ⊥ ( SAC )
A

C
O
B

Activity 4: Exercise 4 / textbooks / 63
- Exercise 4 / textbooks / 105?

- How to prove the plane
perpendicular lines?

OA ⊥ OB
⇒?
OA ⊥ OC
 BC ⊥ OH
⇒?
-
 BC ⊥ OA
- CA ⊥ BH , AB ⊥ CH
-

- Reply
-ERU slant award
-Comment
* Edit perfection
-Burn receive knowledge

- ⇒ OA ⊥ ( OBC ) ⇒ OA ⊥ BC

- ⇒ BC ⊥ ( AOH ) ⇒ BC ⊥ AH

Problem 4/ book/ 105


- Conclude
Call of the intersection K AH and
BC
OH highway square tgiac AOK

anything?
-Tuonng Highway itself is OK
square tgiac OBC anything?
Conclude ?

- H is directly interested triangle ABC

1
1
1
=
+
2
2
OH
OA OK 2
1
1
1
=
+
2
2
OK
OB OC 2

A
C

H

O
K
B

Activity 5: Exercise 5 / textbooks / 105
Exercise 5 / textbooks / 105?
- How to prove the plane
perpendicular lines?

 SO ⊥ AC
 AB ⊥ SH
⇒ ?,
⇒?
 SO ⊥ BD
 AB ⊥ SO

-

- Exercise 6 / textbooks / 105?-

 BD ⊥ AC
⇒ ? , BD ⊥ ( SAC ) ⇒ ?

 BD ⊥ SA

- Exercise 7 / textbooks / 105?

 BC ⊥ AB
 BC ⊥ AM
⇒ ?,

⇒?
-
 BC ⊥ SA
 AM ⊥ SB
- BC ⊥ SB, MN / / BC ⇒ ?

- Reply
-ERU slant award
-Comment
* Edit perfection
-Burn receive knowledge

Problem 6/ book/ 105 :

- SO ⊥ ( ABCD ) , AB ⊥ ( SOH )
- ⇒ BD ⊥ ( SAC ) ⇒ BD ⊥ SC
- IK / / BD ⇒ IK ⊥ ( SAC )

Problem 7/ book/ 105 :

- BC ⊥ ( SAB ) , AM ⊥ ( SBC )
 MN ⊥ SB

-  AM ⊥ SB ⇒ SB ⊥ ( AMN ) ⇒ SB ⊥ AN


Consolidation: The substance has been learned?
Reminding: View and bi episode solved.

Date of preparation:

Date of teaching:

Problem 5/ book/ 105 :

Period 36:
I. Objectives requires:

TEST 45 minutes

Problem 8/ book/ 105 :


• Students understand the method of calculating the angle between two lines, the angle between the two vectors
and the angle between the straight lines and planes.
• Students understand the method of proof line perpendicular to the line and a line perpendicular to the plane.
II. The method means
• Method: Writing paper
• Vehicles: Ruler, calculator, photo subject all students and parents.
III. Process Unit:
1. A stable organization
2. Grasping the spirit:
- Take the serious, highly concentrated.
- Stop the pen immediately after collection command post.
3. Theme: so¹n : 23\3\2009
Problem 1 : ( 6 points)
Given a square cuboid ABCD.A'B'C'D' has AB=3cm
a) Compute angle between two the lines AC and AB'.
b) Compute angle between two the lines AB vµ A'C'.
c) Compute angle between the line DD' and the plane (ABCD)
Problem 2 : (4 points):

Given the pyramid S.ABCD whose base is square of side a. The side SB is perpendicular with the plane (ABCD).
Angle between the line SB and the plane (ABCD) is 600 . In the side SA takes a point M and in the segment SC
SM SN
.
=
SA SC
a. Prove that the faces of the pyramid S.ABCD are the right triangles.
b. Prove MN ⊥ mp ( SBD) .
c. Determining angle between SD and mp(ABCD), then compute the length of the edges of the pyramid.
d. Draw BK ⊥ SO , O is intersection of AC and BD, prove that BK ⊥ mp ( SAC ) .
takes a point N such that:

Problem 1:
Draw figure:

Answers:


D

A

C

B

D'

A'

C'

B'

a) We have AC = AB' = B'C = 3 2 Should triangle AB'C the equilateral triangle.
Thus the angle between AC and AB' is equal to CAB' = 600.
b) We have AB // A'B' Should the angle between AB and A'C' is the angle between A'B' and A'C' is the angle
C'A'B' =450. Since triangles A'B'C' weight square at B'.
c) Because ABCD.A'B'C'D 'cube should DD' perpendicular to the plane (ABCD). Thus the angle between DD 'and
(ABCD) is: 900.
Problem 2:
Because SB square with the bottom should have SB ⊥ AB, SB ⊥ BD ⇒VSAB and VSBD perpendicular at B.
Because ABCD is square so BA ⊥ AD; BC ⊥ CD according 3 perpendicular theorem we have
SA ⊥ AD; SC ⊥ CD inferred VSAD square at A and VSCD square at C.
a. Since SB ⊥ ( ABCD ) ⇒ SB ⊥ AC and AC ⊥ BD ⇒ AC ⊥ ( SBD )
SM SN
=
⇒ MN // AC ⇒ MN ⊥ ( SBD)
Other items by
SA SC
b. Because SB is perpendicular so BD or projection on the bottom is BD
S
¼ = 600 , SB = BD tan 600 = a 2. 3 = a 6
SBD
BD
a 2
=
= 2a 2
0
1

cos 60
2
2
2
2
SA = SB + AB = 6a 2 + a 2 = 7a 2 ⇒ SA = a 7 = SC
a. So AC ⊥ ( SBD) according above so prove AC ⊥ BK
Since BK ⊥ SO hypothetically ⇒ BK ⊥ ( SAC )
SD =

N
M
K
B

C
O

A

Date of preparation:
Date of teaching:
Period 37 TWO PERPENDICULAR PLANES
I) Objectives
1) Knowledge: The angle between two planes perpendicular Sides pahngr
2) Skills:

D

- Determine the angle between two planes
- Demonstrate two perpendicular planes
- Drawing and spatial imagination
3) Thinking: logical, know the familiar strange about
4) Attitude: Contacts are many problems in real life with the image transformation. There are many creative,
interested in learning and actively promote independence in learning
II) Preparation of teachers and students
1) Preparation of Teachers: Lesson Plans, suggestive questions, exercises more
2) Prepare the student: faculty Soch hours, rulers, compasses.
III) The method of teaching: Tip opening combination with oral presentations
IV) The process of teaching
1) stable layers: Check sizes, utensils
2) Check the old thread:
3) Newlesson:
ACTIVITIES TEACHER AND
CONTENT
ACTIVITIES STUDENT
I/ Angle between two planes:
1.
Definition (book). If (α ) //( β ) then angle
Answer: There are three relative position between two
between two planes equal to O0
planes: parallel, overlap and intersect

nm
β

Two straight
lines a and b is
related how the

two planes
phẳng?
- Two straight lines a and b, respectively in two planes and
the intersection angle cuungvuong at a point
- Students summary assumptions, conclusions and
problems
Answer hours according the guidance of any staff
- Students read the contents of the properties and
summarize observations and drawing teacher


- Students summary assumptions, conclusions and answer
the problem according the guidance of teachers
Giải:

a) SA ⊥ ( ABCD ) ⇒ ( SAB ) ⊥ ( ABCD )

( SAC ) ⊥ ( ABCD )
( SAD ) ⊥ ( ABCD )
SA ⊥ ( ABCD ) ⇒ SA ⊥ BD

⇒ BD ⊥ ( SAC )

⇒ ( SBD ) ⊥ ( SAC )

4) strengthened and guided learning at home
- Determine the angle between two planes
- Demonstrate two perpendicular planes
- Drawing and spatial imagination
Date of preparation:

Date of teaching:
Period 38
Two perpendicular planes (next)
I) Objectives
1) Knowledge: The angle between the plane of the two perpendicular planes
2) Skills:
- Determine the angle between two planes
- Demonstrate two perpendicular planes
- Drawing and spatial imagination
3) Thinking: logical, know the familiar strange about


4) Attitude: Contacts are many problems in real life with the image transformation. There are many creative,
interested in learning and actively promote independence in learning
II) Preparation of teachers and students
1) Preparation of Teachers: Lesson Plans, suggestive questions, exercises more
2) Prepare the student: faculty Soch hours, rulers, compasses.
III) The method of teaching: Tip opening combination with oral presentations
IV) The process of teaching
1) stable layers: Check sizes, utensils
2) Check the old thread:
3) Newlesson:
Activity 1 : Right prisms, rectangle cuboids and square cuboids
ACTIVITIES TEACHER AND
CONTENT
ACTIVITIES STUDENT
III. Right prisms, rectangle cuboids and square
cuboids:
1/ Definition:(book)
- Definition is the same book

-activity 4 book?
-activity 5 book?
-Reading example in book?
Lă ng trụ
Lăng trụ đứ ng
Lăng trụ đề u
-Does Problem given, require?
-Draw figure?
M

B

2 / Comments:
Hình lập phương
Hình hộ p chữ nhật
-See Textbook,
answer
-Comment
ERU slant award
-Comment
* Edit perfection
Burn receive knowledge

A

Hình hộp đứ ng

C
N

D
S
B'

C'
P

R
A'

D'

Q

Activity 2: Regular pyramids and regular truncated pyramids.
ACTIVITIES TEACHER AND
CONTENT
ACTIVITIES STUDENT
-See Textbook, answer
IV. Regular pyramids and regular truncated
-Comment
pyramids:
Burn receive knowledge
1/ Regular pyramids: (book)
ERU slant award
- Definition is the same book.
-Comment
- Activity 6 in book?
* Edit perfection
- Activity 6 in book?

Burn receive knowledge
Comment :
S
Episode 2's problem / textbooks / 113?
-To For what? What do you want ?
-Drawing ?

M

A5

A6

A1

A4

H
A2

-Reply
ERU slant award
-Comment
* Edit perfection
Burn receive knowledge

A3

2/ regular truncated pyramids: (book)
S

A' 5

A' 6
O'

A' 1
M'

A' 2

A6
A1

A' 4
A' 3

A5
A4

O
M

A2

A3