1. 5.2 Proving Triangles are Congruent: SSS and SAS

2. WARM UP
∆QRS ≅ ∆LMN. Name all pairs of congruent corresponding parts. Name the three sides of ∆ABC.
QR  LM, RS  MN, QS  LN, Q  L, R  M, S  N

3. Objective
SWBAT show triangles are congruent using SSS and SAS.

4. Side-Side-Side Congruence Postulate

5. Use the SSS Congruence Postulate
From the diagram you know that HJ ≅ LJ and HK ≅LK.
By the Reflexive Property, you know that JK ≅ JK
Yes, there is enough information given. You can use the SSS Congruence postulate to conclude that ∆HJK ≅ ∆LJK

6. Side-Angle-Side Congruence Postulate

7. Use the SAS Congruence Postulate
𝑮𝑯 ≅ 𝑮𝑭
𝑮𝑬 ≅ 𝑮𝑬
<GEH ≅ <GEF
𝑨𝑩 ≅ 𝑩𝑪
<ABD ≅ <CBD
𝑫𝑩 ≅ 𝑫𝑩
You cannot conclude that
∆GHE ≅ ∆GFE because the congruent angles are not between the congruent sides.
Using SAS you can conclude that ∆ABD ≅ ∆CBD

8. You Try
State if the two triangles are congruent. If they are, state how you know. 1) 2) 3)
Yes by SSS
Yes by SAS
Not Congruent

9. You Try
State if the two triangles are congruent. If they are, state how you know. 4) 5) 6)
Not Congruent
Yes by SSS
Yes by SAS

10. A proof is a convincing argument that shows why a statement is true
A proof is a convincing argument that shows why a statement is true. A two-column proof has numbered statements and reasons that show the logical order of the argument. Each statement has a reason listed to its right.

11. 3. Vertical Angle Theorem
STATEMENTS
Reasons
1. Given
2. Given
3. Vertical Angle Theorem
4. Definition of Midpoint
5. SAS Congruence Postulate

12. Reflexive Property of Congruence SSS Congruence Postulate
Write a Proof
Given
Reflexive Property of Congruence
SSS Congruence Postulate

13. Vertical Angles Theorem SAS Congruence Postulate
You Try
Given
AC ≅ DC
Vertical Angles Theorem
SAS Congruence Postulate