Q3-Module 4 Math 8 Illustrating The SSS, SAS and ASA Congruence Postulates

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)
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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.

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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.
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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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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 ≅

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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

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

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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?

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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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