Math 8

1. Mathematics 8
Quarter 3 – Module
5
March 15, 2022
Solving Corresponding
Parts of Congruent
Triangles

2. Prayer

3. Which pair of triangles are congruent?
1
7
2
4
6
5
8
3

4. Which pair of triangles are congruent?
1
7
2 3
4
6
5
8

5. Solving
Corresponding
Parts of Congruent
Triangles

7. B R I D G E

8. Solving Congruent Parts of a
Triangles
Triangles are widely used in our structures.
Bridge is one of them. Triangles make the
structure sturdy (strongly and solidly built). San
Juanico Bridge is one of them.
San Juanico Bridge, known as the longest bridge
in the Philippines, begun its construction in 1969
and finished in 1973. It costs some $22M (Php 154
M in the 70’s). This bridge ranges 2.2 kilometers
and connects the twin island of Leyte and Samar. It
even withstood the power of typhoon Yolanda in
2013 and very evident that it contributes to the

9. Solving Congruent Parts of a
Triangles
Triangles are widely used in our structures.
Bridge is one of them. Triangles make the
structure sturdy (strongly and solidly built). San
Juanico Bridge is one of them.
San Juanico Bridge, known as the longest bridge
in the Philippines, begun its construction in 1969
and finished in 1973. It costs some $22M (Php 154
M in the 70’s). This bridge ranges 2.2 kilometers
and connects the twin island of Leyte and Samar. It
even withstood the power of typhoon Yolanda in
2013 and very evident that it contributes to the

10. Illustrative Examples:
A. The triangles shown below are congruent.
1. Find
2. Find
3. Find
1. Find
By the definition of congruent
segments, the measurements of the
sides are equal.

11. Illustrative Examples:
A. The triangles shown below are congruent.
1. Find
2. Find
3. Find
2. Find
By the definition of congruent
segments, the measurements of
the sides are equal.

12. Illustrative Examples:
A. The triangles shown below are congruent.
1. Find
2. Find
3. Find
3. Find
By the definition of congruent
segments, the measurements of
the sides are equal.
Congruent segments have equal measurements.

13. Illustrative Examples:
B. In the figure,
1. Find
2. Find
3. Find
∠𝑀 𝐴𝐻≅∠𝑇𝐴𝐻
By the definition of congruent angles,
the measurements of the angles are
∠𝑇𝐴𝐻 =
1. Find

14. Illustrative Examples:
B. In the figure,
1. Find
2. Find
3. Find
∠𝑀≅∠𝑇
By the definition of congruent angles,
the measurements of the angles are
equal.
∠M
2. Find

15. Illustrative Examples:
B. In the figure,
1. Find
2. Find
3. Find
∠𝑀 𝐻 𝐴≅∠𝑇𝐻𝐴
∠M𝐻A
3. Find
 The total measurement of the
interior angles of a triangle is 180°.

16. Illustrative Examples:
C. Without an illustration, suppose
The perimeter of is 81mm, = 15mm, = 37mm,
m C = 37 and m = 56
Find the following:
1.
Perimeter of a Triangle = + +
81= + +
81= +
= 29mm

17. Illustrative Examples:
C. Without an illustration, suppose
The perimeter of is 81mm, = 15mm, = 37mm,
m C = 37 and m = 56
Find the following:
2.
= 29mm
3.
= 15mm

18. Illustrative Examples:
C. Without an illustration, suppose
The perimeter of is 81mm, = 15mm, = 37mm,
m C = 37 and m = 56
Find the following:
4.
= 37mm
5.m
B C
B = 37

19. Illustrative Examples:
C. Without an illustration, suppose
The perimeter of is 81mm, = 15mm, = 37mm,
m C = 37 and m = 56
Find the following:
6. m
mB + mG + M = 180
37 + mG+ 56 = 180
93 + mG = 180
mG = 87
7.m
G H
H = 87

20. D. Given: RPA NUJ, RP = 2x + 5 and NU = 13.
∆ ≅ ∆
Find the value of x.
2x + 5 = 13
2x = 13 -5
2x = 8
2 2
x = 4
Illustrative Examples:

21. Illustrative Examples:
E. Given: ACN GMP, m
∆ ≅ ∆ A = (3x – 10) ° and
m G = 32°. Find the value of x.
AG
3x - 10 ° = 32 °
3x =42
3 3
x = 14
3x = 32+10

22. Illustrative Examples:
F. Given: HPE HPO, EH = (4x + 5) mm
∆ ≅ ∆
and OH = (3x + 12) mm.
𝐸𝐻≅OH
4X + 5 = 3X + 12
x = 7
4X – 3X = 12 - 5
1.Find the value of x.
2.What is EH and OH?
EH = 4x + 5
EH = 4(7) + 5
EH = 33
OH = 3x + 12
OH = 3(7) + 12
OH = 33

23. Illustrative Examples:
G. Given: GKN PNK, m
∆ ≅ ∆ G = (5x – 16) ° and m
P=2X+32°.Find the value of x.Find mG and mP
GP
5x - 16 ° = 2X + 32 °
3x =48
3 3
x = 16
5x - 2X = 32 + 16

24. Illustrative Examples:
G. Given: GKN PNK, m
∆ ≅ ∆ G = (5x – 16) ° and m
P=2X+32°.Find the value of x.Find mG and mP
m G = (5x – 16) °
m G = [5(16) – 16] °
m G = 80 – 16
m G = 64 °

25. Illustrative Examples:
G. Given: GKN PNK, m
∆ ≅ ∆ G = (5x – 16) ° and m
P=2X+32°.Find the value of x.Find mG and mP
m P = (2x + 32) °
m P = [2(16) + 32]°
m G = 32+32
m G = 64 °

28. a. = ____
b. = ____
c. = ____
d. = ____
e. = ____
f. m= ____
g. a = ____
h. m= ____
i. m= ____
j. The perimeter of DOG is 82cm, find
∆ .
1. CAT DOG, find the following
∆ ≅ ∆
measurement
7y
3y + 20
5a
2a + 3
3
18
5
35
35
9
1
5
85
29cm

29. a. = ____
b. = ____
c. = ____
d. = ____
e. = ____
f. m= ____
g. a = ____
h. m= ____
i. m= ____
j. The perimeter of DOG is 82cm, find
∆ .
1. CAT DOG, find the following
∆ ≅ ∆
measurement
7y
3y + 20
5a
2a + 3
3
18
5
35
35
9
1
5
85
29cm

30. 2. WXV ZYV, find the following
∆ ≅ ∆
measurement
b
c
d
e

32. 2. WXV ZYV, find the following
∆ ≅ ∆
measurement
84
5
4 4
4
4
5
𝒂=𝟗