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

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

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.

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)

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

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

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

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

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

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

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 .

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

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

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

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 .

< 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

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 .

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

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