4.02 Proof on Congruent Triangles.pdf - Geometry Writing...

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Unformatted text preview: Geometry Writing Assignment: Proofs on Congruent Triangles Each proof is worth 10 points Total Points: 50 Complete a two column proof for each problem. 1. Given: AB ≅ AD and CA ≅ EA Prove: Δ ABC ≅ Δ ADE Statements: PROOFS Line AB congruent to Line AD: GIVEN Line CA congruent to Line EA: GIVEN Angle CAB and Angle DAE are vertical angles: DEFINITION OF VERTICAL ANGLES Angle CAB congruent to DAE: VERTICAL ANGLE THEOREM Triangle ABC congruent to Triangle ADE: SIDE-ANGLE-SIDE CONGRUENCE POSTULATE 2. Given: ∠BCD ≅ ∠EDC and ∠BDC ≅ ∠ECD Prove: Δ BCD ≅ Δ EDC Statements: PROOFS Angle BCD is congruent to Angle EDC: GIVEN Angle BDC is congruent to Angle ECD: GIVEN Line Segment CD is congruent to Line Segment CD: REFLEXIVE PROPERTY OF EQUALITY Triangle BCD is congruent to Triangle EDC: ANGLE-SIDE-ANGLE CONGRUENCE POSTULATE 3. Given: D is the midpoint of AC , ∠BDC ≅ ∠BDA . Prove Δ ABD ≅ Δ CBD Statements: PROOFS D is the midpoint of BD: GIVEN Line Segment AD=DC: DEFINITION OF MIDPOINT Angle BDC is congruent to angle BDA: GIVEN Line Segment BD is congruent to Line Segment BD: REFLEXIVE PROPERTY OF EQUALITY Triangle ABD is congruent to Triangle CBD: SIDE-ANGLE-SIDE CONGRUENCE POSTULATE 4. Given: PG ≅ SG and PT ≅ ST . Prove: ∠GPT ≅ ∠GST Statements: PROOFS Line Segment PG is congruent to Line Segment SG: GIVEN Line Segment PT is congruent to Line Segment ST: GIVEN Line Segment GT is congruent to Line Segment GT: REFLEXIVE PROPRETY OF EQUALITY Triangle GPT is congruent to Triangle GST: SIDE-SIDE-SIDE CONGRUENCE POSTULATE Angle GPT is congruent to angle GST: CPCTC POSTULATE 5. Given: AB // CD , ∠B ≅ ∠D and BF ≅ ED . Prove: Δ ABF ≅ Δ CED Statements: PROOFS Line Segment AB is parallel to Line Segment CD: GIVEN Angle B is congruent to Angle D: GIVEN Line Segment BF is congruent to Line Segment CD: GIVEN Angle A and Angle C are alternative interior angles: DEFINITION OF ALTERNATIVE ANGLES Angle A is congruent to Angle C: ALTERNATIVE INTERIOR ANGLES THEOREM Triangle ABF is congruent to Triangle CED: AAS CONGRUENCE POSTULATE ...
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