DETAILED LESSON PLAN IN MATHEMATICS 8

3RD QUARTER - WEEK 7

Grade & Section: 8 - Diamond Date: February 3, 2025
Allotted time: 1 hour Time: 7:30am - 8:30am
Content Standard
The learner demonstrates understanding of key concepts of axiomatic
structure of geometry and triangle congruence.

Performance Standard
The learner is able to 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 (MELC)

The learner proves statements on triangle congruence. (M8GE-IIIh-1)

I. OBJECTIVES
At the end of the lesson, the learners must have:
1. identified statements on triangle congruence; and
2. proved statements involving (a) multiple angles, (b) isosceles triangle, (c)
overlapping triangles.

II. SUBJECT MATTER

Topic: Proving Statements on Triangle Congruence
References: Mathematics 8 Learner’s Module, Mathematics 8 Teacher’s
Guide, Mathematics 8 Curriculum Guide p. 90 /
https://depedtambayan.net/wp-content/uploads/2022/01/MATH8-Q3-
MODULE7.pdf
https://depedtambayan.org/grade-8-teachers-guide-tg-k-to-12-curriculum/
https://depedbohol.org/v2/wp-content/uploads/2016/03/Math-CG_with-
tagged-math-equipment.pdf
Materials: Cartolina Visual Aids, Cartolina Cut-outs, Markers, Chalk
Value focus: Collaboration, Accuracy, Critical Thinking, Appreciation

III. PROCEDURES
TEACHER’S ACTIVITY LEARNER’S ACTIVITY
A. Preliminary Activities
1. Prayer
Please all stand for the prayer. Student A will lead the prayer.

2. Greetings
Good morning, class. Good morning, ma’am.

3. Checking of Attendance
Is anyone absent? None, ma’am.
 Very good.

4. Classroom Rules Reminder

Before we begin, let me remind
you again the rules to be
observed in my class.

1. Always be on time
2. Keep your classroom clean
3. Be attentive and participative
4. Be respectful
5. Raise your hand if you want to say
something

B. Review
Last meeting, we have discussed
about ‘Proving Two Triangles are
Congruent’. So, how do we prove We can prove it by using triangle
that the two triangles are congruence postulates and
Congruent? theorems.

That’s correct! Speaking of The triangle congruence

triangle congruence postulates postulates are SSS, ASA, and SAS,
and theorems, what are they? while the triangle congruence
theorems are AAS, HyA, HyL, LA,
and LL.
Very good!
Now, how should we organize our We should organize it with a two-
proof? column proof, with statements in
the first column and reasons in the
second column.
That’s right! It seems that you really
understood our previous lesson.

C. Motivation
Before we proceed to our next
lesson, let’s do an activity first. This
activity is entitled “Valid or Not.”
Are you excited, Grade 8? Yes, ma’am!

Mechanics:
The class is divided into five groups,
each assigned one statement with its
reason from a given two-column proof.
Each group selects a representative to
answer whether their assigned
statement is valid or not and explain
their reasoning. Other groups may
agree, challenge, or ask questions. The
teacher confirms the correct answers
and provides clarification. Accurate
justifications will have rewards.

Activity 1. “Valid or Not”

Given: Isosceles ∆��� with respect to the

vertex ∠T, AR ≅ SR
Prove: ∠ATR ≅ ∠STR

Proof:
Statements Reasons
1. Isosceles ∆STA 1. Given
with respect to
the vertex ∠T
2. AT ≅ ST 2. Definition of
Isosceles Triangle
3. TR ≅ TR 3. Refelexive
Property 2. Valid
3. Valid
4. AR ≅ SR 4. Given
4. Valid
5. ∆ATR ≅ ∆STR 5. SAS
5. Not Valid ( It should be SSS)
Congruence
6. Valid
Postulate
6. ∠ATR ≅ ∠STR 6. CPCTC

Good job everyone! Did you enjoy Yes, we did, ma’am!

the activity?

That’s good to hear.

D. Presentation of the Lesson

Let us now move on to our next
lesson which is all about Proving
Statements on Triangle
Congruence.

So, are you ready grade 8? Yes, we are!

Fantastic!
E. Discussion
Proving statements on triangle
congruence is like constructing wooden
roof trusses—each piece must align
precisely to ensure stability and strength.

Just like what the carpenter is doing in

this this picture.

What shapes do you see in the

roof structure? Triangles!

Yes, the dominant shapes are

triangles. We can also see
overlapping triangles and multiple
angles, right? Yes. Ma’am.

Why do you think builders use They use triangles to ensure

triangles instead of squares or stability, strength, balance, and
other shapes for the roof frame? equal distribution of weight.

Very good!

What do you think would happen

if the triangles in this roof were not The roof might collapse, be
congruent (not the same size and unstable, or not fit properly.
 shape)?
That’s right!

How do you think proving triangle It ensures accuracy, maintains

congruence helps engineers and equal measurements, and
carpenters in construction? provides safety.

Very good!
Just as the trusses depend on
accurate measurements for
structural integrity, triangle
congruence relies on specific
criteria to prove that two triangles
are identical in size and shape.

In our previous lesson, we used triangle

congruence postulates and theorems to
prove triangle congruence. Now, let's
apply them to statements involving
multiple angles, isosceles triangles, and
overlapping triangles.

We go first with multiple angles.

Multiple angles refer to two or more

angles within a geometric figure, often
sharing common sides or vertices. In
triangle congruence proofs, multiple
angles are used to establish relationships
between triangles, such as when two
triangles share a common angle or
when angle pairs are given to apply the
ASA or AAS postulates.

Example 1

∠��� ≅ ∠���
 ∠��� ≅ ∠���

∆��� and ∆��� are congruent by SAS

Congruence Postulate and by CPCTC,
∠��� ≅ ∠���.

So, here class, take note that we are

proving the congruency of the
corresponding parts of two triangles. In
this case, with multiple angles involved.
Yes, ma’am.
Can you follow class?

Let’s now proceed to proving

statements involving isosceles triangle.

An isosceles triangle is a triangle with at

least two congruent sides and two equal
base angles.

In isosceles triangles, the Base Angles

Theorem states that the angles opposite
the congruent sides are equal. This helps
prove congruence using the SAS or ASA
postulates. If two isosceles triangles share
a common side or angle, the SSS or AAS
postulate may also be applied.

Example 2
To justify that ∠3 = ∠4, we are given with
�� ≅ ���� by definition ∆��� is an isosceles
triangle and if two sides of an isosceles
triangle are congruent, then the angles
opposite them are also congruent. Since
the two triangles has common side, by
reflexive property, the segment is
congruent to itself. We are also given
that � is a midpoint at ����. By definition,
the segment is divided into two
congruent segments. Thus, we can use
this to justify the congruence of the
corresponding sides and the
congruence of the corresponding
angles of the triangles. Now based on
this, we can use the SAS congruence
theorem to justify the congruence of the
triangles. When two triangles are
congruent, corresponding parts of
congruent triangles are also congruent.
Thus, another pair of corresponding
angles are congruent by CPCTC.

So, do you understand, class? Yes, ma’am.

Let’s now proceed to proving

statements involving overlapping
triangles.

Overlapping triangles are triangles that

share a common side or angle, often
requiring the Reflexive Property to prove
their congruence.

Example 3:
 Given: ∠DAB ≅ ∠CBA,
∠BDA ≅ ∠CAB
Prove: DA ≅ CB
∠D ≅ ∠C

Satetements Reasons
1. ∠DAB ≅ ∠CBA, 1. Given
∠BDA ≅ ∠CAB
2. AB ≅ BA 2. Reflexive
property of
Equality
3. ∆DAB ≅ ∆CBA 3. ASA Postulate
3. DA ≅ CB 4. CPCTC
∠D ≅ ∠C

This proof shows that △DAB is congruent

to △CBA using the ASA Postulate and
then applies CPCTC to conclude that
∠D ≅ ∠C.

First, it is given that ∠DAB ≅ ∠CBA and

∠BDA ≅ ∠CAB. Since these are two
pairs of corresponding angles, they help
establish congruence between the
triangles. Next, BA ≅ BA by the Reflexive
Property, as it is a common side shared
by both triangles. With two angles and
the included side being congruent, the
ASA Postulate confirms that △DAB ≅
△CBA. Finally, by CPCTC
(Corresponding Parts of Congruent
Triangles are Congruent), the
corresponding angles ∠D and ∠C must
also be congruent. This completes the
proof.

So, Do you understand class?

Yes, ma’am.
F. Application
 Now, I want you to answer this
activity by applying what you
have learned from our discussion.

Activity 2. Prove It!

Directions: Prove the following

statements.

1. Given: ∠CAB ≅ ∠DAB, #1 Solution:

∠CBA ≅ ∠DBA Satetements Reasons
Prove: AC ≅ AD 1. ∠CAB ≅ ∠DAB, 1. Given
∠CBA ≅ ∠DBA
A
2. AB ≅ AB 2. Reflexive
property of
Equality
3. ∆ABE ≅ ∆CBD 3. ASA Postulate
4. AC ≅ AD 4. CPCTC
C B D
#2 Solution :
2. Given: DB ≅ OY, ∠2 ≅ ∠1
Prove : ∠��� ≅ ∠���

∠��� ≅ ∠���
3. Given: AE ≅ CD, ∠CDB ≅ ∠AEB
Prove: AB ≅ CB #3 Solution:
Satetements Reasons
3. AE ≅ CD, 2. Given
∠CDB ≅ ∠AEB
4. ∠B ≅ ∠B 2. Reflexive
property of
Equality
3. ∆ABE ≅ ∆CBD 3. AAS Postulate
5. AB ≅ CB 4. CPCTC

G. Generalization
Very well done, class. Now, let’s
do the recap of our lesson by
answering these questions:
 What is the significance of proving Proving triangle congruence
triangle congruence? ensures accuracy in geometric
reasoning and is essential in real-
world applications like
construction and design.

Why is it unnecessary to prove all Triangle congruence postulates

six corresponding parts of two use only three specific parts
triangles to establish congruence? because the remaining parts will
automatically be congruent if the
conditions are met.
Very well done, class!
It seems that you have a deeper
understanding of what we have
discussed today.

Now, I want you to get 1/2 sheet

of pad paper for our quiz.

III. EVALUATION

Quiz #2
Directions: Fill in the correct statements in the blanks. (10 minutes)

(After 10 minutes) Students pass their papers.

Pass your papers class.
 Now, class, please take out your
assignment notebook and copy
your assignment.

IV. ASSIGNMENT

Directions: Read the problem carefully. Explain how the carpenter can prove that
the two triangular supports are congruent in a two-column proof.

Problem:
A carpenter makes two identical triangular supports for a table. How can he prove
that the two triangles are congruent? Which triangle congruence postulate can he
use?

So, that’s all for today. Goodbye Good bye, ma’am. Good bye,
class! classmates. See you tomorrow.

Prepared by:

DAILYN E. EVANGELES
Student Teacher

Noted:

JOAN B. BARRIENTOS
Cooperating Teacher