IV. Materials
Manila paper
Marker]
V. Instructional Strategy
Discussion
VI. Procedure
Session 1
- Introduce the three special kinds of parallelograms.
- Direct the students on explore on page 308 of the textbook.
- Prove Theorem 4-6: The diagonals of a rectangle are congruent
- Practice Exercises
Prove:
- Theorem 4-7: Each diagonal of a square bisects a pair of opposite angles
- Theorenm 4-8: The diagonals of a rhombus are perpendicular
VII. Assignment
Prove Theorems 4-9 and 4-10
Sessions 2
- Preliminary activities
- Check the assignment
- Recall the SAS Postulate and theorem 2-8
- Follow-up Lessons
- Guide the students in proving Theorem 4-11: If the diagonals of a parallelogram is a rhombus.
- 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
- 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.
- Checking for Understanding
Solve Written Mathematics of Exercise 4.2 (numbers 9-14) on pages 312-313 of the textbook.
- 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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- Discuss the proof of theorem 4-12.
- 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
- Preliminary Activities
- Check the assignments
- Recall Theorems 2-1. the definitions of between and the definition of midpoint.
- 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
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?
- Guide the students in proving the mid-segment Theorem.
- illustrative Example
Use the example on page 321 of the textbook.
- 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.
- 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
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
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
Activity 2
1. Give each student a photocopy of this activity.
2. Name the first one l3 and the second l4
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