Δ  by SAS and SSS. Review of  Δs Triangles that are the same shape and size are congruent. Each triangle has three sides and three angles. If all six.

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Presentation transcript:

Δ  by SAS and SSS

Review of  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.

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

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

Objectives Use the SSS Postulate Use the SAS Postulate

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 .

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

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

Statements Reasons________ 1. QR  UT, RS  TS, 1. Given QS=10, US=10 2. QS = US 2. Substitution 3. QS  US 3. Def of  segs. 4. ΔQRS  ΔUTS 4. SSS Postulate Example 1:

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 .

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

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

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

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

Statements Reasons________ 1. RS  RQ; ST  QT1. Given 2. RT  RT2. Reflexive 3. Δ QRT  Δ SRT3. SSS Postulate Q R S T

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