Proving Δs are  : SSS and SAS

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

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

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

Proof Statements Reasons 1. 1. given 2. QS=US 2. subst. prop. = 3. Seg QS  seg US 3. Def of  segs. 4. Δ QRS  Δ UTS 4. SSS post

Side-Angle-Side Postulate (SAS) 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, and C  X, then ΔABC  ΔZXY. ) ( C A X Z

Given: seg WX  seg. XY, seg VX  seg ZX, Prove: Δ VXW  Δ ZXY 1 2 Y V

Proof Statements Reasons 1. seg WX  seg. XY 1. given seg. VX  seg ZX 2. 1  2 2. vert s thm 3. Δ VXW  Δ ZXY 3. SAS post

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

Proof Statements Reasons 1. Seg RS  seg RQ 1. Given seg ST  seg QT 2. Seg RT  seg RT 2. Reflex prop  3. Δ QRT  Δ SRT 3. SSS post

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

Proof Statements seg DR  seg AG Seg AR  seg GR 2. seg DR  Seg DR 3.DRG & DRA are rt. s 4.DRG   DRA 5. Δ DRG  Δ DRA Reasons Given reflex. Prop of   lines form 4 rt. s 4. Rt. s thm 5. SAS post.