Illustrating SAS, ASA, and SSS.

1. ILLUSTRATING THE
SAS, ASAAND SSS
CONGRUENCE
POSTULATE

2. At the end of the
lesson, you are
expected to:

3. Activity 1: Choose me correctly!
1. Write a congruence statement for the triangles.
A. ΔLMN  ΔRTS
B. ΔLMN  ΔSTR
C. ΔLMN  ΔRST
D. ΔLMN  ΔTRS

4. 2. Name the corresponding congruent angles for the
congruent triangles.
A. L  R, N  T, M  S
B. L  R, M  S, N  T
C. L  T, M  R, N  S
D. L  R, N  S, M  T

5. 3. Given ∆𝑅𝑂𝐹, what is the included angle between
𝑅𝑂 𝑎𝑛𝑑 𝑂𝐹?
A.∠𝐹
B.∠𝑂
C.∠𝑅
D.∠𝐹𝑅𝑂
4. In ∆𝑁𝐸𝑇, what side is included between ∠𝑁 and ∠𝑇?
A.𝑁𝑇
B.𝑁𝐸
C.𝐸𝑇
D.𝑇𝐸

6. 5. Given that ΔABC  ΔDEF, which
of the following statements is true?
A. A  E
B. C  D
C. AB  DE
D. BC  FD

7. INCLUDED AND
NON-INCLUDED
PARTS OF
TRIANGLE

8. INCLUDED
ANGLE L
S
Y
Example 1
𝐿𝑆 𝑎𝑛𝑑 𝑌𝑆
𝐿𝑌 𝑎𝑛𝑑 𝑌𝑆
𝐿𝑌 𝑎𝑛𝑑 𝐿𝑆
1.In this figure the included angle of
𝐿𝑆 𝑎𝑛𝑑 𝑌𝑆 is ∠𝑆.
2.The included angle of 𝐿𝑆 𝑎𝑛𝑑 𝑌𝑆 is ∠𝑌.
3.And the included angle of 𝐿𝑆 𝑎𝑛𝑑 𝑌𝑆 is ∠𝐿.

9. What is your observation to example number 1?
OBSERVATION:
The common vertex or common endpoint of the two named sides
is the included angle.
Example 2
𝐸𝐽 𝑎𝑛𝑑 𝐸𝑀
𝑀𝐽 𝑎𝑛𝑑 𝐸𝑀
𝐸𝐽 𝑎𝑛𝑑 𝐽𝑀
1.The common vertex of 𝐸𝐽 𝑎𝑛𝑑 𝐸𝑀
is ∠𝐸.
2.The common vertex of 𝑀𝐽 𝑎𝑛𝑑 𝐸𝑀
is ∠𝑀.
3.The common vertex of 𝐸𝐽 𝑎𝑛𝑑 𝐽𝑀 is
∠𝐽.

10. INCLUDED
SIDE
It is lies between two named angles of the triangle.
L
E
I
∠𝐸 𝑎𝑛𝑑 ∠𝐼
∠𝐿 𝑎𝑛𝑑 ∠𝐼
∠𝐸𝐿𝐼 𝑎𝑛𝑑 ∠𝐼𝐸𝐿
Example 1:
1. In this figure the included side of
∠𝐸 𝑎𝑛𝑑 ∠𝐼 is 𝐼𝐸
2. The included side of ∠𝐿 𝑎𝑛𝑑 ∠𝐼 is
𝐼𝐿
3. And the included side of
∠𝐸𝐿𝐼 𝑎𝑛𝑑 ∠𝐼𝐸𝐿 is 𝐸𝐿

11. What is your observation to example number 1?
OBSERVATION:
The VERTICES of the two named angles determine an included
side.
Example 2
∠𝑁 𝑎𝑛𝑑 ∠𝐴
∠𝑅 𝑎𝑛𝑑 ∠𝐴
∠𝑁 𝑎𝑛𝑑 ∠𝑅
1. The included side of ∠𝑁 𝑎𝑛𝑑 ∠𝐴 is 𝑁𝐴
2. The included side of ∠𝑅 𝑎𝑛𝑑 ∠𝐴 is 𝑅𝐴
3. And the included side of ∠𝑁 𝑎𝑛𝑑 ∠𝑅 is 𝑁𝑅

12. TRIANGLE CONGRUENCE
POSTULATE
SSS
SAS
ASA

13. TRIANGLE CONGRUENCE
POSTULATE
SSS
SIDE-SIDE-
SIDE
If three sides of one
triangle are congruent
to the three
corresponding sides of
another triangle, then
the two triangles are
congruent.

14. TRIANGLE CONGRUENCE
POSTULATE
SSSSIDE-SIDE-
SIDE If three sides of one
triangle are congruent
to the three
corresponding sides of
another triangle, then
the two triangles are
congruent.
𝑺𝑯 ≅ 𝑵𝑴
𝑯𝑨 ≅ 𝑴𝑰
𝑺𝑨 ≅ 𝑵𝑰
∆𝑺𝑯𝑨 ≅ ∆𝑵𝑴𝑰
S
H A N
M I

15. TRIANGLE CONGRUENCE
POSTULATE
SAS SIDE-ANGLE-
SIDE
If two sides and the
included angle of a
triangle are congruent
to the corresponding
two sides and the
included angle of
another triangle, then
the two triangles are
congruent.
A
Y
N R
H
T
83° 83°
𝑌𝐴 ≅ 𝐻𝑅
∠𝐴 ≅ ∠𝑅
𝐴𝑁 ≅ 𝑅𝑇
∆𝑌𝐴𝑁 ≅ ∆𝐻𝑅𝑇

16. TRIANGLE CONGRUENCE
POSTULATE
AS
A
ANGLE-SIDE-
ANGLE
If two angles and the
included side of a
triangle are congruent
to the corresponding
two angles and the
included side of another
triangle, then the two
triangle are congruent.
∠𝑆 ≅ ∠𝐴
𝑆𝑅 ≅ 𝐴𝑁
∠𝑅 ≅ ∠𝑁
∆𝑆𝑅𝐿 ≅ ∆𝐴𝑁𝐸
N
E
A
L R
S

17. D E T E R M I N E N E C E S S A R Y PA R T S T O
S H O W C O N G R U E N C E B E T W E E N
T R I A N G L E S
∆𝐿𝑌𝑆 ≅ ∆𝐿𝐼𝑆
∆𝐿𝑌𝑆 ≅ ∆𝐿𝐼𝑆
∠𝑌 ≅ ∠𝐼
∆𝐿𝑌𝑆 ≅ ∆𝐿𝐼𝑆
𝐿𝑌 ≅ 𝐿𝐼
S
I
L
Y

18. Assignment:
R
L
I
E
a. 𝑅𝐼 ≅ 𝑅𝐿
b. ∠𝐼 ≅ ∠𝐿
c. __________
∆𝑅𝐸𝐼 ≅ ∆𝑅𝐸𝐿 𝑏𝑦 𝑆𝐴𝑆

19. Assignment:
a. 𝐿𝐽 ≅ 𝐴𝑌
c. __________
∆𝐿𝐽𝑌 ≅ ∆𝐴𝑌𝐽 𝑏𝑦 𝑆𝑆𝑆
L
A
Y
J
b. 𝑌𝐽 ≅ 𝑌𝐽

20. THANK
YOU!