4.3 Proving Δs are  : SSS and SAS pg. 212. Remember?  As of yesterday, Δs could only be  if ALL sides AND angles were  NNOT ANY MORE!!!! TThere.

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Presentation transcript:

4.3 Proving Δs are  : SSS and SAS pg. 212

Remember?  As of yesterday, Δs could only be  if ALL sides AND angles were  NNOT ANY MORE!!!! TThere are two short cuts to add.

Post. 19 Side-Side-Side (SSS)  post If 3 sides of one Δ are  to 3 sides of another Δ, then the Δs are .

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

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

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

Post. 20 Side-Angle-Side post. (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. B A C X Y Z ) (

Given: seg WX  seg. XY, seg VX  seg ZX, Prove: Δ VXW  Δ ZXY 12 W V X Z Y

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. Q R S T

Proof Statements Reasons 1. Seg RS  seg RQ1. Given seg ST  seg QT 2. Seg RT  seg RT2. Reflex prop  3. Δ QRT  Δ SRT3. SSS post

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

Proof Statements 1.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 1.Given 2.reflex. Prop of  3.  lines form 4 rt.  s 4. Rt.  s thm 5. SAS post.

Assignment