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
… the triangles.

6. Assignment Geometry: Pg. 195 #9 – 16, 22 - 27
Pre-AP Geometry: Pg. 195 #9 – 16, 22 – 27,

7. So, to prove Δs  must we prove ALL sides & ALL s are  ?
Fortunately, NO!
There are some shortcuts…

8. 4.4 Proving Δs are  : SSS and SAS

9. Objectives
Use the SSS Postulate
Use the SAS Postulate

10. 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 .

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

12. 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

13. Example 1: 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. ΔQRS  ΔUTS SSS Postulate

14. 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 .

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

16. 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

17. Example 2: Statements Reasons_______ 1. WX  XY; VX  ZX 1. Given
2. 1   Vert. s are 
3. Δ VXW  Δ ZXY SAS Postulate 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

19. Example 3: Statements Reasons________ 1. RS  RQ; ST  QT 1. Given
2. RT  RT Reflexive
3. Δ QRT  Δ SRT 3. SSS Postulate Q S R T

20. Given: DR  AG and AR  GR Prove: Δ DRA  Δ DRG.
Example 4:
Given: DR  AG and AR  GR Prove: Δ DRA  Δ DRG. D R A G

21. Example 4: Statements_______ 1. DR  AG; AR  GR 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 Postulate D R G A

22. Assignment Geometry: Pg. 204 #7, 8, 10, 14 – 16, 22 - 25
Pre-AP Geometry: Pg. 204 #12, 14 – 18,