1. Sections 4.3- 4.4 Congruent Triangle Laws SSS, SAS, ASA, and AAS

2. Objectives Name and label corresponding parts of congruent triangles
Identify congruence transformations
Use Tringle Congruence SSS, SAS, ASA, and AAS

3. What are  Δs? Definition of Congruent Triangles:
Triangles that are the same shape and size are congruent.
Remember:
Each triangle has three sides and three angles.
If all six of the corresponding parts are congruent then the triangles are congruent.

4. CPCTC CPCTC – Corresponding Parts of Congruent Triangles are Congruent
Be sure to label  Δs with proper mappings (i.e. if D  L, V  P, W  M, DV  LP, VW  PM, and WD  ML then we must write ΔDVW  ΔLPM)

5. Congruence Transformations
Congruency amongst triangles does not change when you…
slide,
turn,
or flip

6. So, to prove Δs  must we prove ALL sides & ALL s are  ?
NO!
There are some shortcuts…
SSS
SAS
ASA
AAS

7. SSS Side-Side-Side  Postulate
If 3 sides of one Δ are  to 3 sides of another Δ, then the Δs are .

8. Example: SSS
If seg AB  seg ED, seg AC  seg EF, & seg BC  seg DF, then ΔABC  ΔEDF. E D F A B C

9. Given: QR  UT, RS  TS, QS = 10, US = 10 Prove: ΔQRS  ΔUTS
Example 1:
Given: QR  UT, RS  TS, QS = 10, US = 10 Prove: ΔQRS  ΔUTS U U Q Q 10 10 10 10 R R S S T T

10. Example 1: Statements Reasons________ QR  UT, RS  TS, 1.
QS=10, US=10
2. QS = US
3. QS  US
4. ΔQRS  ΔUTS

11. SAS  Side-Angle-Side 
If 2 sides and the included  of one Δ are  to 2 sides and the included  of another Δ, then the 2 Δs are .

12. Example: SAS
If seg BC  seg YX, seg AC  seg ZX, & C  X, then ΔABC  ΔZYX. B Y ) ( A C X Z

13. 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

14. Example 2: Statements Reasons_______ 1. WX  XY; VX  ZX 1.
2. 1  
3. Δ VXW  Δ ZXY W Z X 1 2 V Y

15. ASA 
If 2 angles and the included side of one Δ are  to 2 angles and the included side of another Δ, then the 2 Δs are .

16. < S  < Q, ST  QT, and < STR  <QTR, then Δ SRT  Δ QRT
Example: ASA
< S  < Q, ST  QT, and < STR  <QTR, then Δ SRT  Δ QRT S Q R T

17. AAS 
If 2 angles and the non-included side of one Δ are  to 2 angles and the non-included side of another Δ, then the 2 Δs are .

18. If DR  AG and < DAR  < DGR Then Δ DRA  Δ DRG.
Example: AAS:
If DR  AG and < DAR  < DGR Then Δ DRA  Δ DRG. D R A G

19. Example Proof #3
Given: < KLJ and < MLJ are right angles; < K  < M Prove: Δ KLJ  Δ MLJ J K L M