Republic of the Philippines

Department of Education
REGION 1
SCHOOLS DIVISION OFFICE OF ALAMINOS CITY
ALAMINOS CITY NATIONAL HIGH SCHOOL
ALAMINOS CITY, PANGASINAN

A DETAILED LESSON PLAN IN MATH 8

March 23 ,2023

I. OBJECTIVES
A. Content Standard
The learner demonstrates understanding of key concepts of axiomatic structure of geometry
and triangle congruence.
B. Performance Standard

The learner is able to:

1. Formulate an organized plan to handle a real-life situation.

2. Communicate mathematical thinking with coherence and clarity in formulating,

investigating, analyzing, and solving real-life problems involving congruent triangles using
appropriate and accurate representations.

Most Essential Learning Competency

 Proves two triangles are congruent. (M8GE-IIIg-1)

C. Learning Objectives
At the end of the lesson, the students should be able to:
1. State the SAA/AAS congruence theorem.
2. Use SAA/AAS congruence theorem to prove that two triangles are
congruent.
3. Apply the two-column proof in proving two triangles are congruent.

II. CONTENT: Proves two triangles are congruent.

GAD Core Message: Shared Equalized Opportunities

III. LEARNING RESOURCES:

A. References: Teacher’s Guide
B. Textbooks: Exploring Math 8, Orlando A. Oronce, Marilyn O. Mendoza, pp. 327-338
C. Other Learning Resources – online resources
D. Materials: Laptop, PPT/slide decks

IV. PROCEDURE:
Teacher’s Activity Student’s Activity
PRE-DEVELOPMENTAL ACTIVITY

A. Reviewing previous lesson

Before we proceed with the new lesson, let us put

on test your understanding and learning of the
previous lesson.

Let’s Try!
Direction: Decide which triangle is congruent to
∆CAT by the ASA Congruence Postulate.

a. ∆DOG
b. ∆GDO b. ∆GDO
c. ∆INF
d. ∆FNI
Excellent!
Always remember in using ASA (Angle-Side-
Angle) congruence postulate is very important to
consider the two angles and one included side of
two triangles in order to conclude that the pairs of
triangles are congruent.

B. Motivational Activity

Question: Can the triangles be proven congruent

with the
information given in the diagram? If yes, state the
postulates or theorem you would use.

The vertical angles are congruent, so two pairs of

angles and a pair of non
-included sides are
congruent. The triangles are congruent by the
AAS
Congruence Theorem.

C. Explain/State the objectives of the lesson.

Our lesson objectives in this topic are:

 State the SAA/AAS congruence
theorem.
 Use SAA/AAS congruence theorem
to prove that two triangles are
congruent.
 Apply the two-column proof in
proving two triangles are congruent.

DEVELOPMENTAL ACTIVITY

A. Establishing a purpose for the lesson

DRILL
Take a look! What do you notice in the given
triangles. Refer to the provided markings on the
given figure.

Students’ answers may vary.

God Job. Now that you have already understand the

Triangle Congruence Postulates and Congruence
Theorem, let us now proceed with our new lesson,
proving two congruent triangles using SAA/AAS
congruence theorem.

B. Presenting Examples/Instances of the

New Lesson

Example: Use the SAA/AAS Congruence

Theorem Given: ∠A ≅ ∠D, ∠C≅ ∠F, and BC ≅ EF
Prove: ∆ABC ≅ ∆DEF
Using the marked figures, can the SAA/AAS
Congruence Theorem be used to show that the
triangles are congruent? Explain.

Solution:
a. In the figure, ∠A ≅ ∠D, ∠C≅ ∠F, and BC ≅ EF .
That SAA/AAS Congruence Theorem can be used
to show that ∆ ABC ≅ ∆≝¿ because BC∧EF are
not included between the congruent angles.

C. Discussing New Concepts and Practicing

New Skills

In this lesson we are going to prove that two

triangles are congruent using SAA/AAS
Congruence Theorem.
Alternate Interior Angle

When two parallel lines are crossed by

a transversal, the pair of angles formed on the
inner side of the parallel lines, but on the opposite
sides of the transversal are called alternate interior
angles. These angles are always equal. 

Segment

Bisector
A segment bisector is a line, a ray, a line segment,
or a point that cuts a line segment at the center
dividing the line into two equal parts.

Now, let us apply the congruence postulates and

theorem in proving congruent triangles using the
illustrative examples below.

Example 1: Use SAA/AAS Congruent Theorem to

prove that the two triangles are congruent.
Given: XQ ‖ TR ; XR bisects QT
Prove: ∆ XMQ ≅ ∆ RMT .

Two-column proof: 1. Given

Statements Reasons
1. XQ ‖ TR 2. Given
2. XR bisects QT
3. Alternate Interior Angle is Congruent
3. ∠Q ≅ ∠T,
∠X≅ ∠R 4.Definition of Segment Bisector
4. QM ≅ TM . 5. SAA/AAS Congruence Theorem

5.
∆ XMQ ≅ ∆ RMT

Example 2: Use SAA/AAS Congruent Theorem to

prove that the two triangles are congruent.
Given: GH ‖ HJ∧∠G ≅ ∠ J
Prove: ∆ G HF ≅ ∆ JFH

1. Given
 Statements Reasons 2. Vertical Angle Theorem
1. GH ‖
HJ ; ∠ G ≅∠ J ; 3. Reflexive Property of Triangle Congruence
2.
∠G FH ≅ ∠ JHF 4. SAA/AAS Congruence Theorem
3. FH ≅ FH
4.
∆ A GHF ≅ ∆ JFH

D. Developing Mastery

Activity: Prove that two triangles are congruent by

completing the two-column proof.
Provide all the necessary reason.

Given:∠ A ≅ ∠C ; BE ≅ BD
Prove: ∆ ABE ≅ ∆ CBD . 1. Given
2. Given
Two-column proof:
3. Vertical Angles Theorem
Statements Reasons
1. ∠ A ≅ ∠C 4.SAA/AAS Congruence Theorem
2. BE ≅ BD
3.
∠ ABE ≅ ∠CBD
4.
∆ ABE ≅ ∆ CBD
Two-column proof:
E. Finding Practical Application and Skills Statements Reasons
in Daily Living 1. AD ‖ Given
BC ; ∠ A ≅ ∠C ;
Activity: Your Turn! Prove me, right! 2. ∠ ADB ≅ ∠CBD Vertical Angle
Direction: Study the figure below. Given that AD ‖ Theorem
BC∧∠ A ≅∠ C . Prove ∆ ABD ≅ ∆ CDB. Use two- 3. DB ≅ DB Reflexive Property of
Triangle Congruence
4. ∆ ABD ≅ ∆ CDB SAA/AAS Congruence
Theorem

column proof. To prove that any triangles are congruent we used:

• The SAA/AAS Congruence Postulate that

states If two angles and non-included side of one
POST-DEVELOPMENTAL ACTIVITY
triangle are congruent to the corresponding parts
of another triangle, then the triangles are
A. Generalization and Abstraction About
congruent.
the Lessons • Other geometric properties, definitions and
theorems to help prove that two triangles are
Learners will give a summary of the lesson
congruent.
Wrapping Up!
• The two-column proof to illustrate the proving.

B. Assessment
Two-column proof:
Direction:
Prove that two triangles are congruent by
completing the two-column proof. Provide all the
necessary reasons.
 Given: XY ≅ XA ;∠ Z ≅ ∠ B
Statements Reasons
Prove: ∆ ZXY ≅ ∆ BXA .
1. Given
XY ≅ XA ; ∠ Z ≅ ∠ B
2. Vertical Angle
∠ ZXY ≅ ∠ BXA Theorem
3. SAA/AAS
∆ ZXY ≅ ∆ BXA Congruence Theorem

C. Additional Activities for Application or

Remediation

Activity: State the four Triangle Postulate and

illustrate it.

V. REMARKS:
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VI. REFLECTION:
A. No. of learners who earned 80% in the formative assessment: ________
B. No. of learners who require additional activities for remediation: _______
C. Did the remedial lesson work? _______ No. of learners who have caught up with the lesson.
________
D. No. of learners who continue to require remediation: _________
E. Which of my teaching strategies worked well? Why did these work?
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F. What difficulties did I encounter which my principal or supervisor can help me solve?
____________________________________________________________________________
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G. What innovation or localized materials did I use/discover which I wish to share with other
teachers?
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Prepared by:

MARLON B. HERNANDEZ JR.

Pre- Service Teacher

Approved by:

WILMA N. CAMBA
Cooperating Teacher