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Δ by SAS and SSS
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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.
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Congruence Transformations Congruency amongst triangles does not change when you… slide, turn, or flip … the triangles.
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So, to prove Δs must we prove ALL sides & ALL s are ? Fortunately, NO! TTTThere are some shortcuts…
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Objectives Use the SSS Postulate Use the SAS Postulate
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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 .
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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
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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
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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:
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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 .
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If seg BC seg YX, seg AC seg ZX, & C X, then ΔABC ΔZXY. B ACX Y Z ) ( More on the SAS Postulate
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Given: WX XY, VX ZX Prove: ΔVXW ΔZXY 1 2 W V X Z Y Example 2:
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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:
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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:
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Statements Reasons________ 1. RS RQ; ST QT1. Given 2. RT RT2. Reflexive 3. Δ QRT Δ SRT3. SSS Postulate Q R S T
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Given: DR AG and AR GR Prove: Δ DRA Δ DRG. D A R G Example 4:
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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:
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