1. Identifying types and proofs using theorems
Triangle congruence
Identifying types and proofs using theorems

2. Side-Side-Side (SSS) Postulate
If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent. 4 4 2 2 3 3 3 3 2 2 4 4

3. More on the SSS Postulate
If AB  ED, AC  EF, & BC  DF, then ΔABC  ΔEDF.
More on the SSS Postulate E D F A B C

4. Side-Angle-Side (SAS) Postulate
If two sides and the included angle of one triangle is congruent to two sides and the included angle of another triangle, then the two triangles are congruent. 2
110° 2
110° 4 4

5. More on the SAS Postulate
If BC  YX, AC  ZX, & C  X, then ΔABC  ΔZXY.
More on the SAS Postulate B Y ) ( A C X Z

6. (ASA) Angle-Side-Angle Congruence Postulate
If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the triangles are congruent.

7. Example 1
Which Postulate can you use to prove the triangles congruent?
A) SSS Postulate B) SAS Postulate
C) ASA Postulate D) not congruent

8. Example 2
Which Postulate can you use to prove the triangles congruent?
A) SSS Postulate B) SAS Postulate
C) ASA Postulate D) not congruent

9. Example 3
Which Postulate can you use to prove the triangles congruent?
A) SSS Postulate B) SAS Postulate
C) ASA Postulate D) not congruent

10. Example 4
Which Postulate can you use to prove the triangles congruent?
A) SSS Postulate B) SAS Postulate
C) ASA Postulate D) not congruent

11. Example 5
Which Postulate can you use to prove the triangles congruent?
A) SSS Postulate B) SAS Postulate
C) ASA Postulate D) not congruent

12. Example 6
Which Postulate can you use to prove the triangles congruent?
A) SSS Postulate B) SAS Postulate
C) ASA Postulate D) not congruent

13. Which Postulate can you use to prove the triangles congruent?
A) SSS Postulate B) SAS Postulate
C) ASA Postulate D) not congruent
Example 7

14. Example 8
Which Postulate can you use to prove the triangles congruent?
A) SSS Postulate B) SAS Postulate
C) ASA Postulate D) not congruent

15. Intro to Proofs

16. Given: QR  UT, RS  TS, QS  US Prove: ΔQRS  ΔUTS
Example 1:
Given: QR  UT, RS  TS, QS  US Prove: ΔQRS  ΔUTS U U Q Q R R S S T T

17. Given: WX  XY, VX  ZX Prove: ΔVXW  ΔZXY
Example 2:
Given: WX  XY, VX  ZX Prove: ΔVXW  ΔZXY W Z X 1 2 V Y

18. Given: RS  RQ and ST  QT Prove: Δ QRT  Δ SRT.
Example 3:
Given: RS  RQ and ST  QT Prove: Δ QRT  Δ SRT. S Q R T