This document discusses triangle congruence postulates and their application. It begins by defining triangle congruence and reviewing key terms. It then explains the three triangle congruence postulates - SSS, SAS, and ASA - and provides examples of applying each one to determine if triangles are congruent. Several activities are included for students to practice identifying corresponding parts of congruent triangles and stating the postulate used. The document emphasizes that triangle congruence is important in real-life applications like architecture, art and engineering. It concludes by asking students if they have any other questions.

1. Mathematics 8
Quarter 3-Module 4
Illustrating the
SAS, ASA, and SSS
Congruence Postulates
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2. What can you say about the pictures?
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3. Objectives:
At the end of this lesson, you are expected to:
◍ identify corresponding parts of two congruent triangles;
◍ illustrate triangle congruence postulates; and
◍ determine the necessary parts to show congruence between
triangles.
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4. 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.
Let us have a review of some important terms
Included Angle
◍ An included angle lies between two named sides of a triangle.
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Included Side
◍ An included side lies between two named angles of the triangle.
Postulate
◍ A postulate is a statement that is assumed true without proof.

5. How would you determine if the two
triangles are congruent ?
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6. Two triangles are congruent if they
have:
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1. exactly the same three sides;
and
2. exactly the same three angles.

7. ASA
Postulate
(Angle-
Side-Angle)
SAS
Postulate
(Side-
Angle-Side)
Triangle Congruence Postulates
SSS Postulate
(Side-Side-
Side)
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8. ASA Postulate (Angle-
Side-Angle)
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The Angle Side Angle Postulate
(ASA) says triangles are congruent if
any two angles and their included side
are equal in the triangles.

9. In the sketch, we have △CAT
and △BUG. Notice that
∠C ≅ ∠B
∠A ≅ ∠U
𝐴𝐶 ≅ 𝑈𝐵
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ASA Postulate (Angle-Side-Angle)
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.

10. SAS Postulate (Side-
Angle-Side)
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The Side-Angle-Side (SAS)
Postulate says that triangles are
congruent if any pair of corresponding
sides and their included angle are
congruent.

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SAS Postulate (Side-Angle-Side)
The two triangles have two pairs
of corresponding sides and
included angle that are
congruent. Hence by SAS
postulate, △JOY and △LAB are
congruent.
From the figure, two triangles
△JOY and △LAB, we see that
𝐽𝑂 ≅ 𝐿𝐴
𝑂𝑌 ≅ 𝐴𝐵
∠O ≅ ∠A

12. SSS Postulate (Side-
Side-Side)
12
The third postulate, Side-Side-Side
Postulate (SSS) says triangles are
congruent if three sides of one
triangle are congruent to the
corresponding sides of the other
triangle.

13. 13
SAS Postulate (Side-Angle-Side)
From the figure, all three sides
in △ABC is equal in measurement
to the three corresponding sides
in △DEF,
𝐴𝐵 ≅ 𝐷𝐸
𝐵𝐶 ≅ 𝐸𝐹
𝐶𝐴 ≅ 𝐹𝐷
The two triangles have all of
corresponding sides congruent.
Hence by SSS postulate, △ABC and
△DEF are congruent.

14. Lets see what you’ve got…
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15. Activity 1: Find My Missing Peace!
◍ Direction: Identify the corresponding parts of the
congruent triangle.
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1. If △QRS =△XYZ by SSS Postulate,
then:
𝑄𝑅 ≅ 𝑋𝑌
𝑅𝑆 ≅
___ ≅ 𝑍𝑋

16. Activity 1: Find My Missing Peace!
◍ Direction: Identify the corresponding parts of the
congruent triangle.
16
1. If △QRS =△XYZ by SSS Postulate,
then:
𝑄𝑅 ≅ 𝑋𝑌
𝑅𝑆 ≅ 𝑌𝑍
𝑆Q ≅ 𝑍𝑋

17. 2. If △MOR =△LES by SAS Postulate, then:
𝑀𝑂 ≅
≅ 𝐿𝑆
∠M ≅
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18. 18
2. If △MOR =△LES by SAS Postulate, then:
𝑀𝑂 ≅ 𝐿𝐸
𝑀𝑅 ≅𝐿𝑆
∠M ≅ ∠L

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3. If △GUD =△BET by ASA Postulate, then:
∠U ≅
≅
𝑈𝐷 ≅

20. 20
3. If △GUD =△BET by ASA Postulate, then:
∠U ≅ ∠E
∠D ≅ ∠T
𝑈𝐷 ≅ 𝐸T

21. Activity 2: Tell Me Why?
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Direction: Study the pairs of triangles below and tell whether
the two triangles are congruent or not and state the reason.
1. Congruent or Not Congruent
by:
Not Congruent

22. Activity 2: Tell Me Why?
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2. Congruent or Not Congruent
by:
Congruent
By ASA

23. Activity 2: Tell Me Why?
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3. Congruent or Not Congruent
by:
Congruent
By SSS

24. Activity 2: Tell Me Why?
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4. Congruent or Not Congruent
by:
Congruent
By SSS

25. Activity 2: Tell Me Why?
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5. Congruent or Not Congruent
by:
Not Congruent

26. Activity 2: Tell Me Why?
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6. Congruent or Not Congruent
by:
Not Congruent

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Real Life Application of Triangle Congruence

28. 28
Based on the video
presentation, is triangle
congruence important in
our lives?

29. 29
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?

30. 30
Any Question
Class?

31. Thanks!
Any questions?
Send your questions on my fb messenger: Jonah Francisco-Quizon
Email me @ jonah.francisco003@deped.gov.ph
0977-494-7152
👍
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