DAILY LESSON PLAN
SCHOOL:
ILIGAN CITY NATIONAL HIGH
SCHOOL
GRADE LEVEL: Grade 8
LEARNING
Mathematics
AREA:
TEACHING DATES: February 13-16, 2024
QUARTER: Q3
By the conclusion of the lesson, the student will achieve the following objectives:
- Identify corresponding parts of two congruent triangles.
I. OBJECTIVES
- Illustrate triangle congruence postulates.
- Determine the essential components required to demonstrate congruence between
triangles.
The student exhibits comprehension of fundamental concepts regarding the
A. Content Standards
axiomatic structure of geometry and triangle congruence.
STUDENT TEACHER: AIMAN T. NAO
B. Performance Standards
The student can effectively convey mathematical reasoning with coherence and
clarity when formulating, investigating, analyzing, and solving real-life problems
related to congruent triangles, utilizing suitable and precise representations.
C. Learning Competencies
Illustrates the SAS, ASA and SSS congruence postulates. M8GE-IIId-e-1
II. CONTENT
III. LEARNING
PROCESS
Geometry
Teacher’s guide, Learner's material
A. References
B. Learner’s Material
IV. PROCEDURES
Project Method
Mathematics 8 Quarter 3: Module 3
Drill: Adding Integers
1. (-5) + (-3) =
2. (-11) + (-3) =
3. (-9) + 4
=
4. 15 + (-5) =
5. (-40) + 10 =
A. Reviewing the previous
lesson or presenting the
new lesson
6. (-12) + (-4) =
7. (-15) + (-7) =
8. (-4) + 15 =
9. 25 + (-15) =
10. (-2) + 28 =
Let us have a review of some important terms
Correspondence
Simply means pairing and matching (↔)
Triangle Congruence
Two triangles are congruent if their corresponding sides are equal in length and their
corresponding interior angles are equal in measure. We use the symbol ≅ to show
congruence.
Postulate
A postulate is a statement that is assumed true without proof.
Included Angle
An included angle lies between two named sides of a triangle.
Included Side
An included side lies between two named angles of the triangle.
B. Establishing a purpose
for the lesson
C. Presenting examples/
instances of the new lesson
The purpose of this lesson is to provide a comprehensive understanding of the SAS
(Side-Angle-Side), ASA (Angle-Side-Angle), and SSS (Side-Side-Side)
congruence postulates in triangles. By the end of the lesson, students will grasp the
significance of these postulates in determining when two triangles are congruent.
The emphasis will be on identifying and applying these congruence criteria through
practical examples and interactive activities, promoting a deeper comprehension of
the relationships between corresponding sides and angles.
Before we study the postulates that give some ways to show that the two triangles
are congruent given less number of corresponding congruent parts, let us first
identify the parts of a triangle in terms of their relative positions.
In ∆SON
S
O
N
∠S is an included angle between ̅𝑁̅a n d ̅𝑂̅.
∠O is an included angle between ̅𝑂̅and ̅𝑂̅.𝑁
∠N is an included angle between ̅𝑁̅and ̅𝑁̅𝑂̅.
̅𝑂̅is an included side between ∠S and ∠O.
̅𝑂̅𝑁is an included side between ∠O and ∠N.
̅𝑁̅is an included side between ∠S and ∠N.
Let’s try!
Activity: Include Me!
Given ∆ACE, can you answer the following questions even without the figure?
1. What is the included angle between ̅𝐶̅and ̅𝐶̅𝐸
?
Ans. ∠C
2. What is the included angle between ̅𝐸̅and ̅𝐶̅?
Ans. ∠A
3. What is the included angle between ̅𝐸̅and ̅𝐸̅𝐶̅?
Ans. ∠E
4. What is the included side between ∠A and ∠E ?
Ans. ̅𝐸̅
5. What is the included side between ∠C and ∠E ?
Ans. ̅𝐶̅𝐸̅
6. What is the included side between ∠A and ∠C ?
Ans. ̅𝐶̅
D. Discussing new
concepts and practicing
new skills #1
Triangle Congruence Postulates
These are the minimum requirements needed to prove the congruency of two
triangles which are composed of various groups of three corresponding congruent
parts.
1. SAS Postulate (Side - Angle - Side)
2. ASA Postulate (Angle - Side - Angle)
3. SSS Postulate (Side - Side - Side)
SAS Postulate (Side - Angle - Side) - The Side - Angle - Side Postulate says that
triangles are congruent if any pair of corresponding sides and their included angle
are congruent.
From the figure, two triangles ∆JOY and ∆LAB, we see that
̅𝑂̅≅ ̅
∠O ≅ ∠A
̅𝑂̅𝑌̅≅ ̅𝐵̅
The two triangles have two pairs of corresponding sides and included angle that
are congruent. Hence by SAS postulate, ∆JOY and ∆LAB are congruent.
Another Example:
̅𝑁̅𝑂̅≅ ̅ , ∠O ≅ ∠A , ̅𝑂̅𝑇̅≅ ̅𝑅̅
Question:
When can you say that two triangles are congruent by SAS congruence postulate?
Answer:
According to the SAS congruence postulate, two triangles are congruent if two
sides and the included angle of one triangle are congruent to two sides and
included angle of the other triangle.
E. Discussing new
concepts and practicing
new skills #2
ASA Postulate (Angle - Side - Angle) - The Angle - Side - Angle Postulate says
triangles are congruent if any two angles and their included side are equal in the
triangles.
In the sketch, we have ∆CAT and ∆BUG, Notice that
∠C ≅ ∠B
̅𝐶̅≅ ̅𝐵̅
∠A ≅ ∠U
The two triangles have two angles congruent and the included side between those
angles are also congruent. Hence by ASA postulate, ∆CAT and ∆BUG are
congruent.
Another Example:
∠A ≅ ∠X
̅𝐵̅≅ ̅𝑌̅
∠B ≅ ∠Y
Question:
When can you say that two triangles are congruent by ASA congruence postulate?
Answer:
If two angles and the included side of one triangle are the same as two angles and
the included side of the other triangle, then the triangles are congruent by ASA
postulate.
F. Discussing new
concepts and practicing
new skills #3
SSS Postulate (Side - Side - Side) - The third postulate, Side - Side - Side
Postulate says triangles are congruent if three sides of one triangle are congruent
to the corresponding sides of the other triangle.
From the figure, all three sides in ∆ABC is equal in measurement to the three
corresponding sides in ∆DEF,
̅𝐵̅≅ ̅𝐸̅
̅𝐵̅𝐶̅≅ ̅𝐸̅𝐹̅
̅𝐶̅ ≅ ̅𝐹̅
The two triangles have all of corresponding sides congruent. Hence by SSS
postulate, ∆ABC and ∆DEF are congruent.
Another Example:
̅𝐵̅≅ ̅𝑌̅
̅𝐵̅𝐶̅≅ ̅𝑌̅𝑍̅
̅𝐶̅≅ ̅𝑍̅
Question:
When can you say that two triangles are congruent by SSS congruence postulate?
Answer:
If three sides of one triangle are congruent to three sides of another triangle, then
the triangles are congruent.
G. Developing Mastery
For a more detailed discussion, I will be grouping you into 5 groups.
This will be 10 minutes group activity. Each group will be given the materials
needed for the activity. After answering, I will call 1 representative in ch group to
discuss their answer.
Part 1: Corresponding congruent parts are marked. Identify what postulate (SSS,
SAS, or ASA) that shows the triangles are congruent.
1.
2.
3.
4.
5.
Part 2: Identify what postulate that shows the triangles are congruent and list down
its congruent parts.
H. Finding practical
applications of concepts
and skills in daily living
The teacher will discuss how triangle congruence postulates applied in real-life
situation.
Real life Applications:
Example: Architects use triangle congruence to ensure that structures are stable
and balanced. The SAS postulate, for instance, helps guarantee that the angles and
sides of supporting structures are congruent, contributing to the overall stability of
a building.
I. Making generalizations
and abstractions about the
lesson
Guide Questions for Generalization
How would you determine if the two triangles are congruent?
Name the 3 triangle congruence postulate?
Can you tell how this lesson may help you in real life?
J. Evaluating Learning
Activity 1: Find my missing piece!
Identify the corresponding parts of the congruent triangle.
1. If ∆QRS ≅ ∆XYZ by SSS Postulate , then
̅𝑅≅ ̅𝑌̅
̅𝑅̅ ≅
≅ ̅𝑍̅
2. If ∆MOR ≅ ∆LES by SAS Postulate , then
̅𝑂̅ ≅
≅ ̅
∠M ≅
3. If ∆GUD ≅ ∆BET by ASA Postulate , then
∠U ≅
≅
̅≅
Activity 2: Tell Me Why?
Direction: Study the pairs of triangles below and tell weather the two triangles are
congruent or not and state the reason.
1. Congruent or Not Congruent
By:
2. Congruent or Not Congruent
By:
3. Congruent or Not Congruent
By:
4. Congruent or Not Congruent
By:
5. Congruent or Not Congruent
By:
K. Assignment/Advance
activities for the next
lesson