This document discusses triangle congruence, including definitions of triangles, corresponding sides and angles, and the four main postulates used to prove triangles are congruent: SSS, SAS, ASA, and SAA. It provides examples of determining if triangles are congruent and finding missing side lengths through algebraic applications of the congruence postulates and theorems. Key ideas covered are the properties of triangles, corresponding parts of congruent triangles, and using congruence rules to solve problems.

1. Ms. Anna Carmela Lavin

3. TRIANGLE
Characteristics
• Has three sides and
three angles
• The three angles
sums up to 180
𝟎

5. 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

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

8. Congruence
of a Triangle

9. }Ways to prove
that Triangles
are Congruent

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

11. R
P
S
Q
U
T
ΔSTUΔPQR 
Congruent or Not
Congruent

12. P
S
T
G
L
M
Congruent or Not
ΔLGMΔPST
Not Congruent

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

14. 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

15. Congruent or Not
ΔABC  ΔDEF
Congruent

16. Congruent or Not
ΔAPQ ΔBQP
Not Congruent

17. Congruent or Not
ΔMPN  ΔQSR
Congruent

18. 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

19. Congruent or Not
ΔPQR  ΔTSR
Congruent

20. Congruent or Not
Congruent

21. Congruent or Not
ΔABC ΔDEF
Not Congruent

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

23. Congruent or Not
Not Congruent

24. Congruent or Not
Congruent

25. Congruent or Not? Explain
Not Congruent

26. Congruent or Not? Explain
Congruent by SAA

27. Congruent or Not? Explain
Congruent by ASA

28. Congruent or Not? Explain
Congruent by SAS

29. Congruent or Not? Explain
Not Congruent

30. Congruent or Not? Explain
Not Congruent

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

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

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

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

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

36. Something to think
1. Are all isosceles congruent?
2. Are all right triangles congruent?
3.Are all equilateral triangles congruent?
4. Can congruence be determined without
measurements?

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

38. Activity
N
M
K
J
L
GIVEN: ∆𝑱𝑳𝑲 ≅ ∆𝑵𝑳𝑴
IF m< 𝑱𝑲𝑳 = 𝟔𝟔 𝟎, then m< 𝑵𝑴𝑳 = ?
IF MN=15 in, then KJ = ?