1. Proving Triangles are Congruent (NOTES)
There should be 5 statements with justification
Given: 𝐴𝐶 ≅ 𝐷𝐵 , ∠𝐴𝐶𝐷≅ ∠𝐵𝐷𝐶
Prove: ∠𝐴≅∠𝐵
Statement #1 is given.
Statement # 2 is also given.
Statement # 3
Reflexive Property
Triangles Sharing A Side
Vertical Angles
Triangles With angles facing each other
Mid-Point
Mid-point is given, triangles connected by a point.
Statement # 4 Congruence Postulates
SSS, SAS, AAS, ASA
Statement # 5 (CPCTC)
Corresponding Parts of Congruent Triangles are Congruent 𝐶 𝐵 𝐴 𝐷
Statements
Justifications
1. 𝐴𝐶 ≅ 𝐷𝐵
Given
2.∠𝐴𝐶𝐷≅ ∠𝐵𝐷𝐶
Given
3. 𝐶𝐷 ≅ 𝐶𝐷
Reflexive Property
4. ∆𝐴𝐷𝐶≅∆𝐵𝐶𝐷
SAS Congruency Postulate 5.
∠𝐴≅∠𝐵
CPCTC

2. Prove: Given: Given: Statement Justification Given Given
What is given? HINT: Markings
Given: N A
Statement
Justification
What is given? HINT: Markings
Given I
Which Property is shown? JUSTIFY
Given
What congruence postulate works?
Reflexive Property
What can we conclude?
SSS
CPCTC

3. Prove: 𝐴𝐷 ≅ 𝐸𝐶 Given: B is the midpoint of 𝐷𝐶 Statement Justification𝐴𝐵 𝐸𝐵 𝐷𝐵 𝐶𝐵
Given (Definition of Midpoint)
∠𝐷𝐵𝐴
∠𝐶𝐵𝐸
Vertical Angles
∆𝐷𝐵𝐴
∆𝐶𝐵𝐸
SAS
𝐴𝐷 ≅ 𝐸𝐶
CPCTC

4. Prove: ∠𝑇≅∠𝑃 Given: R is the midpoint of 𝑆𝐼 Statement Justification∠𝑆 ∠I 𝑆𝑅 𝐼𝑅
Given (Definition of Midpoint)
∠𝑇𝑅𝑆
∠𝑃𝑅𝐼
Vertical Angles
∆𝑇𝑅𝑆
∆𝑃𝑅𝐼
ASA
∠𝑇≅∠𝑃
CPCTC

5. Prove: ∠𝑂≅ ∠P
Statement
Justification

6. Prove:
Prove:
∠𝐴≅∠𝐶
∠𝑄≅∠𝑁

7. Prove: ∠𝑅≅ ∠𝑃 R
Statement
Justification T I P
SHOW ALL YOUR WORK

8. Prove: ∠𝐾≅ ∠M
Statement
Justification
SHOW ALL YOUR WORK

9. Prove:
Prove:
∠𝐷≅∠𝐸
∠𝐺≅∠I

10. Prove: Prove: Prove: Prove: ∠𝑂≅∠𝑃 ∠𝐿≅∠𝐽 ∠𝑋≅∠𝑅 ∠𝑆≅∠𝑊
Given: U is the midpoint of 𝑆𝑊 T R I

11. Prove: ∠𝑇≅ ∠𝑅 T P
Statement
Justification I R
SHOW ALL YOUR WORK

12. In ∆MON the 𝑚∠𝑀 53° & 𝑚∠O 90°. Write the sides of the ∆ in descending order:
In ∆ROD the 𝑚∠𝑅 46° & 𝑚∠O 95°. Write the sides of the ∆ in descending order:
If two sides of a triangle re 9 and 17, which of these can not be the third side of the triangles? Explain why? 9, 18, 21, 26, 35
If two sides of a triangle re 21 and 30, which of these can not be the third side of the triangles? Explain why? 51, 10, 18, 49, 53, 12
In triangle PQR, PQ>QR & QR > RP. Which angle in triangle PQR has the smallest measure

13. In ∆MON the 𝑚∠𝑀 60° & 𝑚∠O 82°. Write the sides of the ∆ in descending order:
In ∆ROD the 𝑚∠𝑅 63° & 𝑚∠O 105°. Write the sides of the ∆ in descending order:
If two sides of a triangle are 32 and 9, which of these can not be the third side of the triangles? Explain why? 9, 25, 28, 26, 41
If two sides of a triangle re 18 and 35, which of these can not be the third side of the triangles? Explain why? 53, 50, 18, 20, 17, 99
In triangle RST, RS>ST & ST > TR. Which angle in triangle PQR has the smallest measure