This document discusses triangle congruence, introducing the Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), and Angle-Angle-Side (AAS) postulates. It illustrates examples of congruent and non-congruent triangles using these postulates. It also covers algebraic applications involving congruent triangles and poses questions for critical thinking.

1. WEEK NO. 4

2. WEEK NO. 4

3. WEEK NO. 4
MELC: Illustrates the SAS, ASA and
SSS congruence postulates.
(M8GE-IIId-e-1)

5. TRIANGLE
Characteristics
• Has three sides and
three angles
• The three angles
sums up to 180𝟎

8. Name the Corresponding sides
and angles
Answer:
According to side
1. 𝑫𝑬 ≅ 𝑨𝑩
2. 𝑩𝑪 ≅ 𝑬𝑭
3. 𝑨𝑪 ≅ 𝑫𝑭
Answer:
According to angles
1. < 𝑨 ≅ < 𝑫
2. < 𝑩 ≅ < 𝑬
3. < 𝑪 ≅ < 𝑭

10. KEY WORDS
1.TRIANGLE
2. CORRESPONDING
3. CONGRUENT

11. Congruence
of a Triangle

12. }Ways to prove
that Triangles
are Congruent

13. SSS CONGRUENCE POSTULATE
Three sides of one triangle are
congruent to the three sides of another
triangle

14. R
P
S
Q
U
T
ΔSTU
ΔPQR 
Congruent or Not
Congruent

15. P
S
T
G
L
M
Congruent or Not
ΔLGM
ΔPST
Not Congruent

16. Congruent or Not
D
E
G
F
ΔDEF  ΔGEF
Congruent

17. SAS CONGRUENCE POSTULATE
If two sides and the included angle of
one triangle are congruent to two sides
and the included angle of another
triangle

18. Congruent or Not
ΔABC  ΔDEF
Congruent

19. Congruent or Not
ΔAPQ ΔBQP
Not Congruent

20. Congruent or Not
ΔMPN  ΔQSR
Congruent

21. ASA CONGRUENCE POSTULATE
If two angles and the included side of
one triangle are congruent to the two
angles and the included side of another
triangle

22. Congruent or Not
ΔPQR  ΔTSR
Congruent

23. Congruent or Not
Congruent

24. Congruent or Not
ΔABC ΔDEF
Not Congruent

25. SAA THEOREM
If the two angles and the nonincluded
side of one triangle are congruent to two
angles and the nonincluded side of
another

26. Congruent or Not
Not Congruent

27. Congruent or Not
Congruent

28. Congruent or Not? Explain
Not Congruent

29. Congruent or Not? Explain
Congruent by SAA

30. Congruent or Not? Explain
Congruent by ASA

31. Congruent or Not? Explain
Congruent by SAS

32. Congruent or Not? Explain
Not Congruent

33. Congruent or Not? Explain
Not Congruent

34. Algebraic Application
L
M N
G F
H
800
(2x)
0
Congruent or Not? Why?
Find x?

35. L
M
N
X
Y
Z
510
(4x)0
Algebraic Application
650
Congruent or Not?
Find x?

36. Algebraic Application
(4x-2) cm
22 cm
Congruent or Not?
Find x?

37. Algebraic Application
N
M
K
J
500
Congruent or Not?
Find x and y?
y
12
x+9

38. Algebraic Application
L
M N
S R
Q
2x+11
3x+9
y+100
(2y− 40)0
Congruent or Not?
Find x and y?

39. Something to think
1. Are all isosceles congruent?

40. Something to think
2. Are all right triangles congruent?

41. Something to think
3. Are all equilateral
triangles
congruent?

42. Activity
Congruent or Not?
Find x and y?
3𝑥 600

43. Activity
N
M
K
J
L
GIVEN: ∆𝑱𝑳𝑲 ≅ ∆𝑵𝑳𝑴
IF m< 𝑱𝑲𝑳 = 𝟔𝟔𝟎, then m< 𝑵𝑴𝑳 = ?
IF MN=15 in, then KJ = ?

44. SUMMARY:
Two triangles are congruent if they have:
 Exactly the same three side and
 Exactly the same three angles.

45. SUMMARY:
But we don’t have to know all three sides and all three
angles
……..usually three out of six is enough

46. There are four ways to find if two triangles are
congruent: SSS, SAS, ASA and AAS

49. Ryan C. Enriquez
Subject Teacher