Tuesday, March 22, 2011

Chapter 4

IV. Materials
            Manila paper
            Marker]
V. Instructional Strategy
Discussion
VI. Procedure
Session 1
  1. Introduce the three special kinds of parallelograms.
  2. Direct the students on explore on page 308 of the textbook.
  3. Prove Theorem 4-6: The diagonals of a rectangle are congruent
  4. Practice Exercises
Prove:
    1. Theorem 4-7: Each diagonal of a square bisects a pair of opposite angles
    2. Theorenm 4-8: The diagonals of a rhombus are perpendicular
VII. Assignment
            Prove Theorems 4-9 and 4-10
Sessions 2
  1. Preliminary activities
    1. Check the assignment
    2. Recall the SAS Postulate and theorem 2-8
  2. Follow-up Lessons
    1. Guide the students in proving Theorem 4-11: If the diagonals of a parallelogram is a rhombus.
    2. Illustrative Examples
a.       ABCD is a parallelogram
AE =2x + 10 and CE= 6x-30
Find AC
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b.      Given: JGNS is a rectangle
E is the midpoint JS
Prove: GEN is isosceles

    1. Practice Excercises
a.       Answer Mental Mathematics of excercises 4.2 (numbers 1-6 ) on page 311 of the textbook
b.      Solve Written Mathematics of Exercise 4.2 (numbers 1-8) of the textbook on page 312 of the textbook.
  1. Checking for Understanding
Solve Written Mathematics of Exercise 4.2 (numbers 9-14) on pages 312-313 of the textbook.
  1. Assignment
Solve Written Mathematics of Exercise 4.2 (numbers 15-20) on pages 312-313 of the textbook

If There is enough time, Solve Challenge Problems of Exercise 4.2 on page 314 o the textbook.
Lesson 4.3
Conditions  Guaranteeing that a Quadrlateral is a parallelogram
(Textbook pages 315-327)
I.                   Mathematical Concepts and Skills
A.    A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel
B.     If bith pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
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C.     If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram.
D.    If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
E.     If the diagonals of a quadrilaterals bisect each other , then the quadrilateral is a parallelogram.
F.      The segment that joins the midpoints of two sides of a triangle is parallel to the third side and is one half of its measure.

II.                Objectives
A, Prove that a quadrilateral is a parallelogram
B. Apply the mid-segment Theorem in problem solving.
III. . Values Integration
                        Determination in attaining a goal
IV.             Materials
Rulers
Protractors
Graphing paper
V.                Instrutional Strategies
A.    Practical work
B.     Discussion
VI.             Procedure
Session 1
A.    Preliminary Activities
!. Check the assignment
2. Recall the definitions of parallelogram, Postulate 15, and the congruence postulates for trangles
B. Lesson proper
!. Tell the students to state the converse of corollary 4-1.2 and Theorems 4-3 and 4-4
2. Ask the students to investigate the converses using rulers, protractors, and graphing paper
3. Prove the converses of corollary 4-1.1, Theorems 4-3, and 4-4.
4. Illustrate how to use these converses to prove that a quadrilateral is a parallelogram.
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  1. Discuss the proof of theorem 4-12.
  2. Practice excercises
Prove Theorems 4-13, 4-14, and 4-15.
C.     Assignment
Solve Written Mathematics of Excercises 4.3 (numbers 1-6) on page 321 of the textbook.

Session 2
  1. Preliminary Activities
    1. Check the assignments
    2. Recall Theorems 2-1. the definitions of between and the definition of midpoint.
  2. Follow-up Lesson
!. Arange the students in pairs, then ask them to do the following activities.
a.       Draw any triangle and name it ABC
b.      Find the midpoint of side AB and label it G
c.       Find the midpoint of Side BC and label it E
d.      Draw segment GE
e.       Find the length of GE and the length of AC
f.       Compare their lengths
g.      Is segment GE parallel to side AC? WHY?
    1. Guide the students in proving the mid-segment Theorem.
    2. illustrative Example
Use the example on page 321 of the textbook.
    1. Practice Excercises
a.       Answer mentalMathematics of Exercise 4.3 (numbers 1-14) on pages 322 of the textbook.
b.      Solve Written Mathematicn he Exercise 4.3 (numbers 7-8) on pages 324-3125 of the textbook.
  1. Assignment
Solve Written Mathenatics of Excercises 4.3 (numbers 9-13) on the pages 324-325 of the textbook.
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/session 3
A.    Preliminary Activities
1.      Check the ssignment
2.      Recall the definitions of parallelogram and Theorems 4-12, and 4-13, 4-14, 4-15.
B.     Follow-up Lesson
1.      Illustrative Examples
Write and Explain the proof of this problem on the board.
Given: DE @ AF
            DE ½½ AF
            EC @ FB
            EC½½ FB
2.      Practice Excercises
Solve Written  Mathematics of Excercises 4.3 (numbers 14 and 15) on page 325 of the textbook.

C.     Checking for understanding
Solve Written Mathematics of exercise 4.3 (numbers16 and 17) of page 325 of the textbook.
D.    Assignment
Solve Written Mathematics of Excrcise 4.3 (numbers 18=24) on page 326-327 of the textbook.
If there is enough time, Challenge Problems of exercise 4.3 on page 327 of the textbook.
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Lesson 4.4
The trapezoid and its properties
(textbook pages 324 337, 2 sessions)
I.       Mahematical Concepts an d skills
A.    A trrapexoid is a quadrilateral with exactly one pair of parallel sides
B.     An isoscleles trapezoid is a trapezoid are congruent
C.     The base abgles of an isosceleles trapezoid are congruent.
D.    The diagonals of an isosceles trapezoid are congruent
E.     If the base angles of trapezoid are congruent, then the trapezoid id isosceles.
F.      If the diagonals o a trapezoid are congruent, the trapezoid is isosceles.
G.    The median of a trapezoid is the segment joining the midpoints of the legs.
H.    The median of a trapezoid is parallel to its bases
I.       The median of a trapezoid is half the sum of the lengths of the bases
ii.                  Objectives
A.    Identify and define a isosceles trapezoid
B.     Apply inductive and deductive skills to derive a certain properties of the trapezoid
C.     Apply the Theorem about trapezoid
III.             Values Integration
The importance of cooperation in performing a task
IV.             Materials
Rulers
Sticks
V.                Instructional Strategies
A.    Practical Work
B.     Discussion
VI.             Procedure
Session 1
A.    Preliminary activities
1.      Check the assignment
2.      Recall the definition opf a trapezoid and Theorem 4-5.
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B.     Lsson Proper
!. Ask the students to from  pairs, distribute four sticks to each pair two cks should have congruent lengths.
2. Have each pair construct a trapezoid
3. Tell them to do the following
      a. Find the lengths of the legs in centimeters
      b. lengths of the diagonbals in centimeters
      b. lengths of the measures of the base angles.

4. When the strudents are finished doing the activity, ask each pair to tell the class about their trapezoid (It is expected that some of them will be able to construct an isosceles trapezoid)
5. Ask the students to define an isosceles trapezoid and to enumerate some of its properties.
6. Guide the students I n proving theorem 4-17.
7. Illustrative Examples
      a. Prove Theorem 4-20
      b. Complete the proof of theorem 4-19.
                        C. Assignment
                                    Prove Theorem 4-20

Session 2

A, Preliminary Activities
            1. Check the assignment
            2. Recall the Mid-degment Theorem
B. Follow-up Lesson
            1. Guide the students in proving Theorem 4-21
            2. Ask the students to work on Expllore on page 332 of the t3extbook
            3. Illustrative Example
                        Use the example on page 331 of the textbook.
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4. Practice Excercises
            a. Answer Mental Mathematics of Exercises 4.4 (numbers 1-14) on page 334 of the textbook.
            b. Solve Written Mathematics of Exercise 4.3 (numbers 1-10) on page 335-336 of the textbook.

C.     Checking for understanding
Solve Written Mathematics of exercises 4.4 (numbers 11-16) on page 337 of the textbook.
D.    Assignment
Solve Written Mathematics of Exercise 4.4 (numbers 17-20) on page 337 of the textbook.

If there is enough time, solve Challenge problems of exercise 4.4 on page 337 of the textbook.

Lesson 4.5
Kite
!.  ematical Concepts and Skills
A.    A kite is a quadrilateral with two distinct pairs of congruent, adjacent sides
B.     If  exactly oone diagonal of a quadrilateral is the perpendicular bisector of the other diagonals are perpendicular.
C.     If a quadrilateral is akite, then its diagonals are perpendicular.
D.    The area of  a kite is half the product of thelengths of its diagonals
II.                Objectives
A.    Defie a Kite 
B.     Prove and supply the theorems related to kites
III.             Values integration
Being helpful and friendly
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IV.             Materials
Picture of a boy flying a kite
Manila paper
Marker
V.                Instructional Strategy
Discussion
VI.             Procedure
Session 1
A.    Preliminary Activities
1.      Check the assignment
2.      Recall the definition of quadrilateral
B.     Lesson Proper
1.      Show a picture of a boy flying a kite
2.      Ask whether a kite csan be considered a quadrilateral.
3.      Ask one student to draw a kite
4.      Ask another student to define a kite based on the figure .
5.      Guide the students in proving theorems 4-34, 4-25, and 4-26.
6.      Practice Excercises
Answer Mental Mathematics of exercise 4.5 (numbers 1-10 ) on page 340-341 of the textbook.
C.     Assignment
Solve Written Mathematics of Excercse 4.5 (numbers1-8) on pages 341 of the textbook.

Session 2
A.    Preliminary Activities
1.      Check the assignments
2.      Recall Theorems 4-25 and 4-26
B.     Follow-up Lesson
1.      Illustrative Example
Solve this problem on the board, Find the area of a kite with diagonals 10cm and 16 cm.
2.      Practice Excercises
Solve Written Mathematics of Exercise 4.5 (numbers 9-11) on page 342 of the textbook.
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`                                               C. Checking for understanding
Solve Written Mathematics of exercise 4.5 ( numbers 12 ) on page 342 of the textbook.
E.     Assignment
Solve written mathematics of exercise 4.5  numbers 13-20) o n page 342- 343 of the textbook.
If there is enough time, solve the challenge problems of exercise 4.5 on page 343 of the textbook.
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Chapter 5       
Similarity
Lesson 5.1
Ratio and Proportion

I.       Mathematical Concepts and skills
A.    A ratio is a comparison of two number sby division
B.     A proportion is a statement of equality between two ratios.
C.     A proportion can be written inyo its equivalent form by using the laws of proportion
D.    The geometric mean of two numbers is the square root of there product
E.     Segment AC and segment DF are said to be divided proportionally by point b on AC and point D on DF if AB:BC=DE:EF
II.                Objectives
A.    Define and simplify the rarios
B.     Define a proportion and identify its parts
C.     Define proportional segments
D.    Define and apply the geometric mean of two numbers
E.     State and apply the fundamental laws of proportion
III.             Values Integration
Resourcefulness
IV.             Materials
Pictures
Birthday cards
Christmas cards
                        V. Instructional Strategy
Whole Class Discussion
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V.                Procedure
Session 1
A.    Preliminary Activities
1.      Check the assignment
2.      Review using linear equations
B.     Lesson proper
1.      Show pictures of the Parthenon of Greece and the Triumphal Arch of Constantine in rome, which approximates two golden rectangles
2.      Tell the students about the golden ration and golden rectangle
3.      Distribute some pictures, birthday cards and old Christmas cards. Ask the students to measure them to to find out if they approximate the golden rectangle
4.      Tell the students that being resourceful not only of teachers but also for the students
5.      Define ration and proportion, Write a proportion and identify its parts
6.      Illustrate the Laws of Proportion
7.      Illustrate Example         
Use the example on page 351 of the textbook.
8.      Practice Exercise
Solve Mental Mathematics of exercise 5.1 (numbers 1-10) on page 359 of the textbook.
C.     Assignment
Solve Written MAthenmatics of exercise 5.1 (numbers 1-4) on page 360 of the textbook.

Session 2
A.    Preliminary Activities
1.      Check the assignment
2.      Recall proportional segmentd
B.     Follow-up Lesson
1.      Illustrative Example
Use the illustrative examples on page 352 of the textbook.
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2.      Practice Excercises
Solve Written /mathematics of exercise 5-1 (numbers 5-8) on page 361 of the textbook
C.     Checking for understanding
Solve written Mathematics of exercise 5.1 (numbers 15-22) on page 363 of the textbook .

Lesson 5.2
Proportionality Theorems

I.       Mathematical Concepts and skills
A.    If two triangles have two equal altitudes, then the ratio of their areas is equal to the ratio of ther bases.
B.     Two triangles on the same base and between two parallels are equal in area
C.     If a line is parallel to one side of a triangle and intersects the other two sides in sistinct points, then it divides the two sides proportionally.
D.    If a line divides two sdes of a triangle proportionally, then the line is parallel to the third side.
II.                Objectives
To prove and apply the proportionality theorem and its converse.
III.             Values Integration
Reliance on one’s ability and judgement
IV.             Materials
Activity sheets
Rulers
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V.                Instructional Strategies
A.    Practical work
B.     Discussion
VI.             Procedure
Session 1
A.    Preliminary work
1.      Check the assignment
2.      Recall the are  Formula for triangles and theorem 4-5
B.     Lesson Proper
Activity 1
I.                   Give each student a photocopy of this activity
a.       Draw two parallel lines. Name the first line l1 and the second line l2
b.      Plot any two points B and I on l2
c.       Plot any two points E and L on L2
d.      Draw BE, BL, IL, and IE.
e.       What geometric figures are formed
f.       Name two overlapping geometric figures.
g.      Do they have the same altitudes? Why?
h.      Do they have the same base?
i.        What can you say about their areas
j.        What can you conclude?
Activity 2
1.      Give each student a photocopy of this activity.
2.      Name the first one l3 and the second l4




Chapter 5

c. Construct two nonoverlapping triangles with different bases between the two parallel lines.
d. Represent the altitude of each triangle by h and their respective bases by b1 and b2.
e. Find the ratio of the areas of the two triangles.
f. What can you conclude?
                Tell the students that in doing the given activities, they should rely on their own abilitiesand judgment.
2. Guide the students in proving Theorem 5-1 and 5-2 and in completing the proof of Basic Proportionality Theorem.
3. Illustrative Examples
                Use the examples on page 366 of the textbook.
4. Practtice Exercises
                a. Answer Mental Mathematics of Exercise 5.2 (numbers 1-10) on page 368 of the textbook.
                b. Solve Written Mathematics of Exercise 5.2 (numbers 1-7) on page 368 of the textbook.
C. Assignment
                Solve Written Mathematics of Exercise 5.2 (numbers 8-10) on page 369 of the textbook.
Session 2
A.      Preliminary Activities
1.       Check the assignment.
2.       Recall the Law of Proportion
B.      Follow-up Lesson
1.       Guide the students in proving the Converse of the Basic Proportionality Theorem.
2.       Practice Exercises
Solve Written Mathematics of Exercise 5.2 (numbers 11 and 12) on page 369 of the textbook.
C.      Checking for Understanding
Solve Written Mathematics of Exercise 5.2 (numbers 13-16) on page 369 of the textbook.
D.      Assignment
Solve Written Mathematics of Exercise 5.2 (numbers 17-20) on page 370 of the textbook.

Lesson 5.3
Similarity Between Triangles
I.                    Mathematical Concepts and Skills
A.      Similar polygons are polygons in which the corresponding  angles are congruent and the ratios of the lenghts of the corresponding sides are equal.
B.      Two triangles are similar, if and only if the corresponding angles are congruent and the lenghts of the corresponding sides are proportional.
C.      If there exists a correspondence between the vertices of two triangles such that three angles of one triangle are congruent to the corresponding angles of the second triangle, respectively, then the two triangles are similar.
D.      If two angles of a triangle are congruent to two angles of the second triangle, respectively, then the two triangles are similar.
E.       Similarity between triangles is an equivalence relation.
F.       If a triangle is similar to a second triangle and a second triangle is congruent to a third triangle, then the first triangle is similar to the third triangle.
G.     If two pairs of corresponding sides of two triangles are propotional and the included angles are congruent , then the two triangles are similar.
H.      If all three pairs of corresponding  sides of two triangles are proportional, then the two triangles are similar.
II.                  Objectives
A.      Illustrate and define similar polygons and similar triangles
B.      Prove and use the AAA similarity and AA Similarity Theorems to draw conclusions about triangles
C.      Show that similarity between triangles is an equivalence relation
D.      Prove that if a triangle is similar to to a second triangle and a second triangle is congruent to a third triangle, then the first triangle is similar to the third triangle
E.       Prove and use the SAS Similarity and SSS Similarity Theorems to draw conclusions about triangles
III.                Values Integration
Self-confidence is necessary to accomplish desired result
IV.                Materials
Picture of similar figures
Manila paper
Marker
V.                  Instructional Strategies
A.      Whole Class Discussion
B.      Practice
VI.                Procedure
Session 1
A.      Preliminary Activities
1.       Check the Assignment.
2.       Recall the congruence Postulate for Trianlges
B.      Lesson Proper
1.       Show the class pictures having the same shape but differnt sizes, Ask the students afterward to describe the pictures.
2.       Then present the following geometric figures:

a.                                                                                    C. 
 

                                                                                                                                         
                                                                                                                                        
                                                                                                                                                                    

b.                                                                                      D.
                                                                                                                                       
 


Ask the students to describe the geometric figures.
3.                   Tell the students that the last pairs of geometric figures are examples of similar polygons. Ask them to define similar polygons.
4.                   Consider the two triangles below .
                                                                      
                                                                                                                                        





Ask the students to describe the triangles.
5.                   Ask the students to complete the proofs of AAA Similarity and AA Similarity Theorems. Tell the students that they should have self-confidence in accomplishing the task given to them.
6.                   Illustrative Examples
Use the examples on page 372 of the textbook.
C.      Practice Exercises
a.       Answer Mental Mathematics of Exercises 5.3 (numbers 1-10)   on pages 380-382 of the textbook.
b.      Solve Written Mathematics of Exercises 5.3 (numbers 1-6)  on pages 382 of the textbook.
D.      Assignment
Solve Written  Mathematics of Exercise 5.3 (numbers 7 and 8) on pages 383 of the textbook.

Session 2
A.      Preliminary Activities
1.       Check the assignment.
2.       Recall the Poin Plotting Theorem and the Line Postulate .
B.      Follow-up Questions
1.       Ask the students to complete the proof of the SAS Similarity Theorem.
2.       Guide the students in proving the SSS Similarity Theorem.
3.       Practice Exercises
 Solve Written Mathematics of Exercise 5.3 (number 11) on page 383 of the textbook.
C.      Assignment
Solve the Written Mathematics of Exercise 5.3 (number 11) on page 383 of the textbook.

Session 3
A.      Preliminary Activities
1.       Check the assignments
2.       Recall the following:
a.       AA Similarity
b.      SAS  Similarity Theorem
c.       SSS Similarity  Theorem
B.      Follow-up Questions
1.       Illustrative Example
Show how to prove this problem.

Given : AB is perpendicular to BD
                EC is perpendicular to CD
Prove : triaangle ABD is congruent to triangle ECD
2.       Practice Exercises
Solve written mathematics of exercise 5.3 (numbers 12 and 13) on page 384 of the text book.
C.      Checking for Understanding
                      Solve written mathematics of exercise 5.3 (numbers 14-20) on page 384 of the text book.       
D.      Assignments
Study the Proof of the right Triangle Similarity Theorem.


Lesson 5.4
Similarities in Right Triangle

I.        Mathematical Concepts and Skills
A.      In any right triangle, the altitude to the hypotenuse divides the triangle into two right triangles which are similar to each other and to the given right triangle.
B.      In a right triangle, the altitude to the hypotenuse is the geometric mean of the segments into which it divides the hypotenuse and each of the leg is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to the leg.
C.      In an isoceles right triangle, the lenght of the hypotenuse is equal to the lenght of the leg times square root of 2.
D.      In a 30-60-90 triangle, the length of the hypotenuse is twice the lenght of the shorter leg and the lenght of the longer leg is square root of 3 times the length of the shorter leg.
II.  Objectives
A.      Find the lengths of sides and altitudes of rifgt triangles
B.      Apply relationships in Isoceles Right Triangle Theorem and right 30-60-90 degrees triangles.
III. Values Integration
 Impotance of cooperation
IV. Materials
marker
Manila paper
V.  Instructional Strategies
      A. Whole Class Discussion
      B. Small Essay  Discussion
VI.  Procedure
Session 1
A.      Preliminary Activities
1.       Check assignments.
2.       Recall the Pythagorean Theorem
B.      Lesson Proper
1.       Ask the students to solve the following problems.
If in triangle ABC, angle ACB is a right angle , line  CD is the hypotenuse to line AB, A is a 60 degrees angle and angle ACD is 30 degrees, find angle DCB and angle B.
2.       Ask the following questions:
a.       Into how many triangles is the given triangle divided by its hypotenuse?
b.      Are the two triangles congruent? Similar? Why?
c.       Are the two triangles similar to the original triangle? Why?
3.       Divide the class into small groups.Remind them about  the importance of cooperation in doing a task. Then tell them to prove the Right Triangle Similarity theorem and the Geometric Mean Theorem.
4.       Illustrative Examples.
Use the examples on page 388 of the book
5.       Practice Exercises
a.       Answer  Mental Mathematics of Exersice 5.4 (numbers 1-10) on page 390 of the textbook.
b.      Solve Written Mathematics of Exercise 5.4 ( numbers 1-9) on page 390 of the textbook.
C.      Assignment
        Solve Written Mathematics of Exercise 5.4 (numbers 10-19) on page 391 0f the textbook.

                      Session 2
A.      Preliminary  Activities
1.       Check the assignment.
2.       Recall the Pythagorean Theorem.
B.      Follow-up Lesson
1.       Prove the Isoceles Rigth Triangle Theorem and the 30 dergee, -60 degree, -90 degree Triangle Theorem.
2.       Illustrative Example
Find the perimeter of triangle ABC.
3.       Practice Exercises
Solve Written Mathematics of Exercise 5.4 (number 20) on page 319 of the textbook.
C.      Checking Understanding
Solve Written Mathematics of Exercise 5.4  (number 21) on page 391 of the textbook.
D.      Assignment
Solve Written mathematics o f Exercises 5.4 (number 22) on page 391 of the textbook.

Lesson 5.5
Consequences of the Basic Proportionality Theorems; Areas and Perimeters of Similar Figures


I.        Mathematical Concepts and Skills
A.      If each of the three or more coplanar parallel lines are each cut by two transversals, the intercepted segments on the two trnsversals are proportional.
B.      The bisector of an angleof a triangle separates the opposite sides into segments whose lengths are proportional to the lengths of the other two sides.
C.      Two corresponding altitudes of similar triangles are proportionalto the corresponding sides.
D.      Any two corresponding angle bisectors of similar triangles are proportional to the corresponding sides.
E.       Any twocorresponding medians of similar triangles are proportional to the corresponding sides.
F.       The ratio of the perimeters of two similar triangles is equal to the ratio of any pair of corresponding sides.
G.     If two triangles are similar, then the ratio of their areas equals the square of the ratio of the lrngths of any corresponding sides.
H.      The ratio of the areas of two similar triangles is equal to the square of the ratio of the two corresponding  perimeters.
II.    Objectives
A.      To prove and apply the theorems about three or more parallel lines cut by a transversal
B.      To prove and apply the Theorem about the bisector of an angle of a triangle
C.      To prove and apply the theaorems about proportional segments in triangles
D.      To prove and apply the theorems about perimeters and areas of similar triangles
III. Values Integration
        The need for self-confidence in performing a task
IV. Materials
        Manila paper
        Marker
V. Instructional Strategies
        A. Whole class discussion
        B. Practice
VI.  Procedure
        Session 1
A.      Preliminary Activities
1.       Check assignments
2.       Recall the basic Proportionality Theorem
B.      Lesson Proper
1.       Ask the students to solve the following problems
2.       Suppose in the above figur, the transversal t1 is moved the right, will the value of QRr change as well as a result of the movement?
3.       Guide the students in proving that if each three or more coplanar parallel lines are cut by two transversals, the intercepted segments of the two transversals are proportional.
4.       Illustrative Example
5.       Practice Exercises
a.        Answer Written  Mathematics of Exercises 5.5 (numbers 1-10)   on page 406 of the textbook.
b.      Answer Written Mathematics of Exercises 5.5 (numbers 1-2)   on page 406 of the textbook.
C.      Assignment
Solve written Mathematics of Exercise 5.5 (number 3) on page 406 of the textbook.
Session 2
A.      Preliminary activities
1.       Check the assignment.
2.       Recall the definition of an angle bisector.
B.      Follow-up Questions
1.       Guide the students in proving the following theorem:
The bisector of an angle of a triangle separates the opposite sides into segments whose lengths are proportional to the lengths of the two other sides.
2.       Illustrative Example
In triangle ABC, ray AD bisects angle BAC.
If AB is 8,AC is 10, and BC is 6 find BD and DC
3.       Practice Exercises
Solve written mathematics of exercises 5.5 (number 4)on page 406 of the textbook.
C.      Assignment
Solve Written Mathematics of Exercise 5.5 (number 5) on page 406 of the textbook.
Session 3
A.      Preliminary  Activities
1.       Check assignments
2.       Recall the AA Similarity Theorem
B.      Follow-up Questions
1.       Guide the students in proving the following theorems:
a.       Any two corresponding  altitudes of similar triangles are proportional to the corresponding sides.
b.      Any two corresponding angle bisectors of similar triangles are proportional to the corresponding sides.
2.       Tell the students that they should have sel-confidence whenever they are asked to prove any geometric statement
Prove the following:
a.       Any two corresponding medians of similar triangles are proportional to the corresponding sides.
b.      The ratio of the perimeters of two similar triangles is equal to the ratio of any pair of corresponding sides.
C.      Complete the proof of Theorem 5-20.
Session 4
A.      Preliminary Activities

1.       Check assignment.
2.       Recall the Geometric mean Theorem.
B.      Follow-up Lesson
1.       Prove th pythagorean Theorem using the geometric Mean theorem.
2.       Introduce the Pythagorean Triples.
3.       Illustrative Example
Find the perimeter and area of triangle ABC.
4.       Practice exercise
Solve Written Mathematics of Exercise 5.5 (number 7) on page 407 of the text book.
C.      Checking for Understanding
                Solve Written Mathematics of Exercise 5.5 (number 8) on page 407 of the textbook.
D.      Assignment
Solve Written Mathematics Exercise 5.5 (numbers 9 and 10) on page 407 of the textbook.