4.02 Writing Assignment Proofs on Congruent Triangles.pdf -...

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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 A is the midpoint of CE A is the midpoint of BD Angle CAB and Angle DAE are vertical angles Angle CAB is congruent with angle DAE Triangle ABC and Triangle ADE are congruent ≅ Δ ADE Given Given Definition of vertical angles Vertical angle theorem SAS Conguent postulate 2. Given: ∠BCD ≅ ∠EDC and ∠BDC ≅ ∠ECD Prove: Δ BCD ≅ Δ EDC Angle BCD + Angle BDC + Angle CBD = 180 Angle EDC + Angle ECD + Angle CED = 180 Triangle BCD is congruent with triangle EDC Interior Angles Theorem Interior Angles Theorem AAA Congruence postulate 3. Given: D is the midpoint of AC , ∠BDC ≅ ∠BDA . Prove Δ ABD ≅ Δ CBD Angle BDC = Angle BDA Segment AD = Segment DC Segment BD = Segment BD Triangle ABD is congruent with triangle CBD Given Given Reflexive Property SAS Congruence Postulate 4. Given: PG ≅ SG and PT ≅ ST . Prove: ∠GPT ≅ ∠GST Segment PG = Semgnet SG Segment PT = Semgent ST Segment TG = Segment TG Triangle GPT is congruent with Triangle GST Angle GPT = Angle GST Given Given Reflexive Property SSS Congruence Postulate Definition of congruence 5. Given: AB // CD , ∠B ≅ ∠D and BF ≅ ED . Prove: Δ ABF ≅ Δ CED Segment BF = Segment ED Angle B = Angle D Angle BAF = Angle ECD Triangle ABF is congruent with Triangle CED Given Given Alternate Interior Angles Theorem AAS Congruence Postulate ...
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