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Proving Δs are : SSS and SAS
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Side-Side-Side (SSS) Postulate
If 3 sides of one Δ are to 3 sides of another Δ, then the Δs are .
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A Meaning: ___ ___ If seg AB seg ED, seg AC seg EF & seg BC seg DF, then ΔABC ΔEDF. B C ___ E ___ ___ D ___ F
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Given: seg QR seg UT, RS TS, QS=10, US=10 Prove: ΔQRS ΔUTS
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Proof Statements Reasons 1. 1. given 2. QS=US 2. subst. prop. =
3. Seg QS seg US Def of segs. 4. Δ QRS Δ UTS SSS post
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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 .
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If seg BC seg YX, seg AC seg ZX, and C X, then ΔABC ΔZXY.
) ( C A X Z
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Given: seg WX seg. XY, seg VX seg ZX, Prove: Δ VXW Δ ZXY
1 2 Y V
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Proof Statements Reasons 1. seg WX seg. XY 1. given seg. VX seg ZX
2. 1 vert s thm 3. Δ VXW Δ ZXY SAS post
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Given: seg RS seg RQ and seg ST seg QT Prove: Δ QRT Δ SRT.
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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
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Given: seg DR seg AG and seg AR seg GR Prove: Δ DRA Δ DRG.
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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.
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