1. CPCTC
Concept 24

2. Corresponding
Parts of
Congruent
Triangles are
Congruent

3. Use the diagram to answer the following.
What triangle appears to be congruent
to PAS?
to PAR?
∆𝑹𝑳𝑺
∆RLP
If 𝑃𝑆 ≅ 𝑅𝑆 and 𝑃𝐿 ≅ 𝐴𝑅 , what additional information would you need to prove PSL  RSA?
If LPA  ARL and PL≅AR, what additional information would you need to prove LPA  ARL?
𝑺𝑳 ≅ 𝑺𝑨
SSS
∠𝑺𝑷𝑳≅∠𝑺𝑹𝑨
SAS
∠𝑷𝑨𝑳≅∠𝑹𝑳𝑨
AAS
∠𝑷𝑳𝑨≅∠𝑹𝑨𝑳
ASA
𝑷𝑨 ≅ 𝑳𝑹
SAS

4. Use the diagram to answer the following questions.
To prove PSL  PSA, which triangles must you prove to be congruent?
To prove SL ≅ 𝑆𝐴 , which triangles must you prove to be congruent?
 LPS  APS
 LPS  APS
 LRS  ARS
 LPS  ARS
 APS  LRS

5. Use the marked diagrams to state the method used to prove the triangles are congruent. Give the congruence statement, then name the additional corresponding parts that could then be concluded to be congruent.
Missing Info/Why:
𝐷𝐵 ≅ 𝐵𝐷
Symmetric Prop.
Triangle Congruence/Why:
∆𝐴𝐵𝐷≅
∆𝐶𝐷𝐵
SSS
CPCTC:
∠𝐴≅ ∠𝐶
∠𝐴𝐵𝐷≅
∠𝐶𝐷𝐵
∠𝐴𝐷𝐵≅
∠𝐶𝐵𝐷

6. Use the marked diagrams to state the method used to prove the triangles are congruent. Give the congruence statement, then name the additional corresponding parts that could then be concluded to be congruent.
Missing Info/Why:
∠𝐴𝐶𝐵≅
∠𝐷𝐶𝐸
Vertical Angles
Triangle Congruence/Why:
∆𝐴𝐵𝐶≅
∆𝐷𝐸𝐶
ASA
CPCTC:
∠𝐵≅ ∠𝐸
𝐴𝐵 ≅ 𝐷𝐸
𝐵𝐶 ≅ 𝐸𝐶

7. Prove: O is the midpoint of 𝑁𝑃 Statements Reasons
Given: 𝑁𝑆 ≅ 𝑃𝑅 and  S  R
Prove: O is the midpoint of 𝑁𝑃
Statements
Reasons 1.
1. Given 2.
2. Given 3.
4. ∆NOS≅ 4. 5. 6.
𝑁𝑆 ≅ 𝑃𝑅
 S  R
∠𝑆𝑂𝑁≅
∠𝑅𝑂𝑃
Vertical Angles
∆POR
AAS
𝑁𝑂 ≅ 𝑃𝑂
CPCTC
Def of a midpoint
O is the midpoint of 𝑁𝑃

8. Given: 𝑊𝑋 ≅ 𝑍𝑋 and 𝑋𝑌 bisects WXZ
Prove: W ≅ Z
Statements
Reasons 1.
1. Given 2.
2. Given 3. 4.
5. ∆WXY≅ 5. 6.
𝑊𝑋 ≅ 𝑍𝑋
𝑋𝑌 bisects WXZ
∠𝑊𝑋𝑌≅
∠𝑍𝑋𝑌
Def of bisect
𝑋𝑌 ≅ 𝑋𝑌
Reflexive
∆ZXY
SAS
W ≅ Z
CPCTC

9. Isosceles and Equilateral Triangles
Concept 25

10. Has exactly three congruent sides
Vertex Angle
the angle formed by the legs.
Leg
Leg
the 2 congruent sides of an isosceles triangle.
Base Angle
2 angles adjacent to the base.
the 3rd side of an isosceles triangle
Base

12. 1. Name two unmarked congruent angles.
BCA is opposite BA and A is opposite BC, so BCA  A.
___
Answer: BCA and A

13. 2. Name two unmarked congruent segments.
___
BC is opposite D and BD is opposite BCD, so BC  BD.
Answer: BC  BD

14. 3. Which statement correctly names two congruent angles?
A. PJM  PMJ
B. JMK  JKM
C. KJP  JKP
D. PML  PLK

15. 4. Which statement correctly names two congruent segments?
A. JP  PL
B. PM  PJ
C. JK  MK
D. PM  PK

17. 5. Find mR.
Since QP = QR, QP  QR. By the Isosceles Triangle Theorem, base angles P and R are congruent, so mP = mR . Use the Triangle Sum Theorem to write and solve an equation to find mR.
Triangle Sum Theorem
mQ = 60, mP = mR
Simplify.
Subtract 60 from each side.
Answer: mR = 60
Divide each side by 2.

18. 6. Find PR.
Since all three angles measure 60, the triangle is equiangular. Because an equiangular triangle is also equilateral, QP = QR = PR. Since QP = 5, PR = 5 by substitution.
Answer: PR = 5 cm

19. A. Find mT.
A. 30°
B. 45°
C. 60°
D. 65°

20. B. Find TS.
A. 1.5
B. 3.5
C. 4
D. 7

21. 7. Find the value of each variable.
mDFE = 60
4x – 8 = 60
4x = 68
x = 17
The triangle is equilateral, so all the sides are congruent, and the lengths of all of the sides are equal.
DF = FE
6y + 3 = 8y – 5
3 = 2y – 5
8 = 2y
4 = y

22. 8. Find the value of each variable.
A. x = 20, y = 8
B. x = 20, y = 7
C. x = 30, y = 8
D. x = 30, y = 7