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Geometry and Trigonometry Proofs Review: Congruence and Midpoint Theorems

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This document contains a series of proofs in geometry involving congruence of triangles and properties of midpoints and parallel lines. The exercises aim to help students demonstrate their understanding of important geometric theorems and postulates. Students are tasked with completing various proofs, including proving triangle congruences knowing that certain segments are parallel or represent midpoints. This review homework serves as an essential practice for mastering key concepts in geometry and preparing for assessments.

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Geometry and Trigonometry Proofs Review: Congruence and Midpoint Theorems

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  1. Geometry/Trig 2 Name __________________________ 4-2, 4-3 Review Homework Date ___________________________ B C Proof #1 Given: AB || CD; AD || CB Prove: ΔABC  ΔCDA 4 3 2 1 A D Statements Reasons 1. ________________________________ 1. ______________________________ 2. ________________________________ 2. ______________________________ 3. ________________________________ 3. Given 4. ________________________________ 4. ______________________________ 5. ________________________________ 5. ______________________________ 6. ________________________________ 6. ______________________________ Proof #2 Given: C is the midpoint of AE C is the midpoint of BD Prove: AB  ED A B C D E Statements Reasons 1. ________________________________ 1. ______________________________ 2. ________________________________ 2. ______________________________ 3. ________________________________ 3. Given 4. ________________________________ 4. ______________________________ 5. ________________________________ 5. ______________________________ 6. ________________________________ 6. ______________________________ 7. ________________________________ 7. ______________________________

  2. Geometry/Trig 2 4-2, 4-3 Review Homework D Proof #3 Given: AC  BD BD bisects ADC Prove: ΔADB  ΔCDB A C B Statements Reasons 1. ________________________________ 1. ______________________________ 2. ________________________________ 2. ______________________________ 3. ________________________________ 3. Given 4. ________________________________ 4. ______________________________ 5. ________________________________ 5. ______________________________ 6. ________________________________ 6. ______________________________ Proof #4 Given: T is the midpoint of CB T is the midpoint of AE Prove: AC || EB C A T Statements Reasons E B 1. ________________________________ 1. ______________________________ 2. ________________________________ 2. ______________________________ 3. ________________________________ 3. Given 4. ________________________________ 4. ______________________________ 5. ________________________________ 5. ______________________________ 6. ________________________________ 6. ______________________________ 7. ________________________________ 7. ______________________________ 8. ________________________________ 8. ______________________________

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