Q3T3.2_Solving Corresponding Parts of Congruent Triangles.pdf

Key Powerpoint of CCSIS in Math 3RD Quarter. 8th Grade Level

1. Solving Corresponding Parts
of Congruent Triangles
QUARTER 3 – TOPIC 3.2
Prepared by: Sir Jerome Cristobal

2. Lesson Objective:
After studying this module, you are expected to:
•Solve Corresponding Parts of Congruent
Triangles (M8GE-IIIf-1)

3. Now that you have learned the different triangle
congruence postulates (SAS, ASA, SSS) and how to
use them to illustrate congruent triangles, we will now
use these postulates to prove that the other
corresponding parts of the two congruent triangles
are congruent. This is known as CPCTC
(Corresponding Parts of Congruent Triangles are
Congruent).
We are going to use these concepts in solving for the
corresponding parts of congruent triangles.

4. 1.Given, ΔABC ≅ΔKLM by ASA Triangle Postulate,
then it follows that…

5. From the statements above, it follows that the
lengths of the corresponding sides and the measures
of the corresponding angles of ΔABC and ΔKLM are
equal. Therefore,
AB = KL
AC = KM
BC = LM
mA = mK
mB = mL
mC = mM.

6. EXAMPLE: Solve for the measure of the missing parts of
congruent triangles.
Solutions:
�?????? ≅��
MI = TO
MI = 12 cm
�� ≅��
DM = PT
DM = 9cm
�?????? ≅��
DI = PO
DI = 15 cm

7. Since T and M are right angles, then they are
equal (all right angles measure 90
0
). And to solve for
the measures of the remaining angles,
 I ≅  O  D ≅  P
m I = m O m D = m P
m I = 37
0
m D = 53
0

8. 2. Given: ΔSAP ≅ΔLET, solve for the value of x and y.
�?????? ≅��
SA = LE
x + 15 = 31
x = 31 – 15
x = 16

�� ≅��
SP = LT
29 = y – 4
29 + 4 = y
33 = y

9. Learning Task 1
1. Given ΔABC ≅ ΔXYZ, solve for the
angles and sides of ΔXYZ.

10. Learning Task 1
1. Given ΔABC ≅ ΔXYZ, solve for the
angles and sides of ΔXYZ.
22cm
50
7456

11. Learning Task 1
2. Given
ΔJPO ≅ ΔSMR,
solve for the
values of v, w, x, y
and z.

12. v= 25cm
25
25
z= 10cm
65

13. Learning Task 2
Given, ΔART ≅ ΔHOP, if m ∠R = 54◦ and m∠T = 73 ◦, HO =
15cm, AT = 10cm.
1. Illustrate the two triangles.
2. What angles of ΔHOP has a measure of 53◦ and a measure of 54◦?
3. Identify the sides with measures equal to HO and AT.
4. If RT= 20cm, find the value of x if OP = 11x – 13
Which is the shortest side of ΔART?

14. Learning Task 2

20. Thank you for listening! God bless!