84470 - Geometry Writing Assignment Proofs on Congruent Triangles Each proof is worth 10 points Total Points 50 Complete a two column proof for each

84470 - Geometry Writing Assignment Proofs on Congruent...

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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 = AD , CA = EA ; Given Angle CAB = Angle DAE ; Vertical Angle Theorem Triangle ABC = Triangle ADE ; SAS congruence 2. Given: ∠BCD ≅ ∠EDC and ∠BDC ≅ ∠ECD Prove: Δ BCD ≅ Δ EDC Angle BCD = Angle EDC ; Given Angle BDC = Angle ECD ; Given CD = CD ; Reflexive Property of Equality Triangle BCD = Triangle EDC ; ASA congruence 3. Given: D is the midpoint of AC , ∠BDC ≅ ∠BDA . Prove Δ ABD ≅ Δ CBD D is midpoint of AC ; Given AD = DC ; Definition of midpoint Angle BDC = Angle BDA ; Given BD = BD ; Reflexive Property of Equality Triangle ABD = Triangle CBD ; SAS congruence 4. Given: PG ≅ SG and PT ≅ ST . Prove: ∠GPT ≅ ∠GST PG = SG ; Given PT = ST ; Given GT = GT ; Reflexive Property of Equality Triangle GPT = Triangle GST ; SSS congruence Angle GPT = Angle GST ; CPCTC 5. Given: AB // CD , ∠B ≅ ∠D and BF ≅ ED . Prove: Δ ABF ≅ Δ CED AB // CD ; Given Angle B = Angle D ; Given BF = ED ; Given Angle A = Angle C ; Alternate Interior Angles are Congruent Triangle ABF = Triangle CDE ; AAS congruence ...
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