ProofsonCongruentTriangles.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 AB is congruent to AD and CA is congruent to EA / Reason: Given Angle DAE is congruent to angle CAB/ Reason: Vertical angles are equal ABC is congruent to ADE/ Reason: SAS 2. Given: ∠BCD ≅ ∠EDC and ∠BDC ≅ ∠ECD Prove: Δ BCD ≅ Δ EDC Angle BCD is congruent to angle EDC and angle BDC is congruent to angle ECD/ Reason: Given CD = CD/ Reason: Reflexive property BCD is congruent to EDC/ Reason: ASA 3. Given: D is the midpoint of AC , ∠BDC ≅ ∠BDA . Prove Δ ABD ≅ Δ CBD D is the midpoint of AC, angle BDC is congruent to angle BDA/ Reason: Given AD is congruent to DC/ Reason: Definition of midpoint BD is congruent to BD/ Reason: Reflexive property ABD is congruent to CBD/ Reason: SAS 4. Given: PG ≅ SG and PT ≅ ST . Prove: ∠GPT ≅ ∠GST PG is congruent to SG and PT is congruent to ST/ Reason: Given GT is congruent to GT/ Reason: Reflexive property Angle GPT is congruent to angle GST/ Reason: SSS 5. Given: AB // CD , ∠B ≅ ∠D and BF ≅ ED . Prove: Δ ABF ≅ Δ CED AB//CD, Angle B is congruent to D and BF is congruent to ED/ Reason: Given ABF is congruent to CED/ Reason: SAS ...
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