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4.3 Proving Δ s are : SSS and SAS. pg. 212. Remember?. As of yesterday, Δ s could only be if ALL sides AND angles were NOT ANY MORE!!!! There are two short cuts to add. Post. 19 Side-Side-Side (SSS) post.
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Remember? • As of yesterday, Δs could only be if ALL sides AND angles were • NOT ANY MORE!!!! • There are two short cuts to add.
Post. 19Side-Side-Side (SSS) post • 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=10Prove: ΔQRS ΔUTS U Q 10 10 R S T
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
Post. 20Side-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 Y ) ( C A X Z
Given: seg WX seg. XY, seg VX seg ZX, Prove: Δ VXW Δ ZXY W Z X 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 QTProve: Δ QRT Δ SRT. S Q R T
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 GRProve: Δ DRA Δ DRG. D R A G
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. Proof