1. 4.3  Δs

2. Objectives Name and label corresponding parts of congruent triangles
Identify congruence transformations

3.  Δs
Triangles that are the same shape and size are congruent.
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
… one of the triangles.

6. So, we can only prove Δs  if ALL sides AND ALL s are .
There are some shortcuts…

7. 4.3 Proving Δs are  : SSS and SAS

8. Objectives
Use the SSS Postulate
Use the SAS Postulate

9. Postulate 4.1 (SSS) Side-Side-Side  Postulate
If 3 sides of one Δ are  to 3 sides of another Δ, then the Δs are .

10. A
SSS Postulate
___
___
If seg AB  seg ED, seg AC  seg EF, & seg BC  seg DF, then ΔABC  ΔEDF. B C
___ E
___
___ D
___ F

11. Given: QR  UT, RS  TS, QS=10, US=10 Prove: ΔQRS  ΔUTS

12. Proof Statements Reasons 2. QS=US 2. Substitution
1. QR  UT, RS  TS, 1. Given
QS=10, US=10
2. QS=US Substitution
3. QS  US Def of  segs.
4. Δ QRS  Δ UTS SSS Postulate

13. Postulate 4.2 (SAS) Side-Angle-Side  Postulate
If 2 sides and the included  of one Δ are  to 2 sides and the included  of another Δ, then the 2 Δs are .

14. SAS Postulate
If seg BC  seg YX, seg AC  seg ZX, & C  X, then ΔABC  ΔZXY. B Y ) ( C A X Z

15. Given: WX  XY, VX  ZX Prove: Δ VXW  Δ ZXY1 2 Y V

16. Proof Statements Reasons 1. WX  XY; VX  ZX 1. Given
2. 1   Vert s Thm.
3. Δ VXW  Δ ZXY SAS Postulate

17. Given: RS  RQ and ST  QT Prove: Δ QRT  Δ SRT.

18. Proof Statements Reasons 1. RS  RQ; ST  QT 1. Given
2. RT  RT Reflexive
3. Δ QRT  Δ SRT 3. SSS Postulate

19. Given: DR  AG and AR  GR Prove: Δ DRA  Δ DRG.

20. Proof Statements Reasons 1. DR  AG; AR  GR 1. Given 2. DR  DR
3.DRG & DRA are rt. s
4.DRG   DRA
5. Δ DRG  Δ DRA
Reasons
1. Given
2. Reflexive Property
3.  lines form 4 rt. s
4. Right s Theorem
5. SAS Postuate

21. Assignment
Pre-AP: Pg. 195 #9 – 16, 22 – 25 Pg. 204 #14 – 19, 22 – 25