This document provides a lesson on solving corresponding parts of congruent triangles. It begins with an introduction and objective. It then presents the theorem that corresponding parts of congruent triangles are congruent. Several examples are worked through to demonstrate identifying congruent angles and sides of triangles and solving for missing values. The lesson concludes with an activity for students to practice solving corresponding parts of congruent triangles.

3. Hi students!
Let’s make Math
fun and exciting!

5. SOLVING CORRESPONDING
PARTS OF CONGRUENT
TRIANGLES
MATHEMATICS 8 - QUARTER 3 – WEEK 5
M8GE-IIIf-1
Prepared by:
MELISSA M. REYES
SST-III/ Math Teacher

6. Objective:
Solves corresponding parts of
congruent triangles.
At the end of the lesson, you are expected to:
1. Identify parts of congruent triangles.
2. Solves corresponding parts of congruent
triangles; and
3. Appreciate the application of congruent
triangles in real-life situations.

7. Theorem: Corresponding Parts of Congruent
Triangles are Congruent (CPCTC)
Triangles are congruent if all corresponding
sides and angles are congruent.
If we prove two triangles are congruent,
then we can state that any of their
corresponding parts are congruent.

8. EXAMPLE #1
A B
C
D
E
F
If ΔABC ≅ ΔDEF, name the congruent angles and
sides. Then draw the triangles, using arcs and slash
marks to show the congruent angles and sides.

9. A B
C
D
E
F
First, name the three pairs of congruent angles by
looking at the order of the vertices in the statement
ΔABC ≅ ΔDEF

10. So, A ≅ D, B ≅ E, and C ≅ F.
Since A corresponds to D, and B corresponds to E.
AB ≅ DE
Since B corresponds to E, and C corresponds to F.
BC ≅ EF
Since A corresponds to D, and C corresponds to F.
AC ≅ DF

11. A B
C
D
E
F
ΔABC ≅ ΔDEF Read as “triangle ABC is congruent to triangle DEF.”
≅ Symbol for congruency
Δ Symbol for triangle.
The congruent corresponding are marked identically.
Can you name the corresponding congruent sides? Corresponding congruent
angles?
Congruent sides: AB ≅ DE, BC ≅ EF, AC ≅ DF
Congruent Angles: A ≅ D, B ≅ E, and C ≅ F.

12. EXAMPLE #2
D
O
G
40°
50°
90°
T
A C
2x +10°
ΔDOG is congruent to ΔCAT. Find the value of x.
Since ΔDOG ≅ ΔCAT, the corresponding part are
congruent wherein O ≅ A .

13. O ≅ A
m O ≅ m A
50 = 2x + 10 Substitution
50 - 10 = 2x + 10 – 10 Subtract 10 from each side
40 = 2x
40 = 2x
2 = 2
Divide each side by 2
20 = x

14. D
O
G
40°
50°
90°
T
A C
2x +10°
20 = x
2x +10° Substitute the value of x
2(20) +10°
40 +10°
50°
m A = 50°

15. EXAMPLE #3
J
F
H
G
2y – 3
6x + 8
2.5
35°
In the diagram, ΔFHJ ≅ ΔHFG. Find the value of x and y.
a. What part of the triangles are congruent?
b. How do we solve for the value of x and y?

16. So, F ≅ H, J ≅ G, and H ≅ F.
Since F corresponds to H, and H corresponds to F,
FH ≅ HF
Since H corresponds to F, and J corresponds to G,
HJ ≅ FG
Since F corresponds to H, and J corresponds to G,
FJ ≅ HG
a.

17. FJ ≅ HG
2y – 3 = 2.5 Substitution
2y -3 + 3 = 2.5 + 3 Add 3 from each side
2y = 5.5
2y = 5.5
2 = 2
Divide each side by 2
y = 2.75
b.

18. J
F
H
G
2y – 3
6x + 8
2.5
35°
y = 2.75
FJ = 2y – 3 = 2.5 Substitute the value of y.
2(2.75) – 3 = 2.5
5.5 – 3 = 2.5
2.5 = 2.5
m FJ = 2.5

19. F ≅ H
m F ≅ m H
6x + 8 = 35 Substitution
6x +8 – 8 = 35 – 8 Subtract 8 from each side
6x = 27
6x = 27
6 = 6
Divide each side by 6
x = 4.5

20. J
F
H
G
2y – 3
6x + 8
2.5
35°
x = 4.5
F = 6x + 8 = 35° Substitute the value of x.
6(4.5) + 8 = 35°
27 + 8 = 35°
35° = 35°
m F = 35°

21. EXAMPLE #4
J
H
K
G
M
If K = 68° and J = x + 10,
find the exact value of x.
K + M+ G = 180°
H + J+ G = 180°
There fore we can say that
K + J+ G = 180°
Substitute the value x
68 + x + 10 + x = 180°
Combine like terms
68 + 10 + x + x = 180°
78 + 2x = 180°
Subtract both sides by 78 to remain 2x only
Add like terms
78 – 78 + 2x = 180° - 78
2x = 102 Divide both sides by 2 to remain x only
2 = 2
x = 51

22. If K = 68° and J = x + 10, find the exact value of
J and G.
To solve for the value of J
J = x + 10
J = 51 + 10
J = 61°
To solve for the value of G
G = x
G = 51
K + M+ G = 180°
H + J+ G = 180°
Therefore:
68 + 61 + 51 = 180°
68 + 61 + 51 = 180°

23. ACTIVITY TIME!
Given: ΔBOY ≅ ΔGRL; solve for the value of x and y, then find the
measure of missing parts of congruent triangles.
O G L
R
B Y
12
(3y – 6)°
48°
93°

24. ANSWER!
Given: ΔBOY ≅ ΔGRL; solve for the value of x and y, then find the
measure of missing parts of congruent triangles.
O G L
R
B Y
12
(3y – 6)°
48°
93°

25. Corresponding sides Corresponding angles
BO = GR
Answer:
BY = GL
OY = RL
B = G
Y = L
O = R
BO = GR
For:
2x + 3 = 11
2x + 3 – 3 = 11- 3
2x = 8
2 = 2
x = 4
For:
BY = GL
BY = 12
OY = RL
15 = RL
For: B = G
93 = 3y – 6
93 + 6 = 3y – 6 + 6
99 = 3y
3 = 3
33 = y
BO = 2x +3
BO = 2 (4) + 3
BO = 8 + 3
BO = 11
G = 3y – 6
G = 3 (33) – 6
G = 99 – 6
G = 93
For:
Y = L
O = R
O = 48°
L = 39°

26. Theorem: Corresponding Parts of Congruent
Triangles are Congruent (CPCTC)
Triangles are congruent if all corresponding
sides and angles are congruent.
If we prove two triangles are congruent,
then we can state that any of their
corresponding parts are congruent.
Remember!

27. Individual Activity
Given: ΔDEF ≅ ΔXYZ; solve for the measure of missing parts of
congruent triangles.
73°
E
F
D 25 cm
47°
Y
X Z

28. That ends our Lesson for today!
Study our next Lesson: Proving two triangles
are congruent.
Good day Everyone!