Question

Match each statement to the reasons given for the geometric proof.

Given: ABCD is a parallelogram

Prove: Diagonals bisect each other(AE=CE and BE = DE
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Answer 1

Answer: 5, 3, 1, 2, 6, 4

Explanation:

The proof should be written as follows (which is a different order than provided):

Statement Reason

1. ABCD is a parallelogram 1. Given

2. AB||DC and AD||BC and AB ≅ DC 2. Definition of parallelogram

3. ∠ABD ≅ ∠CDB 3. Alternate Interior Angles Theorem

4. ∠DEC ≅ ∠BEA 4. Vertical Angles Theorem

5. ΔABE ≅ ΔCDE 5. AAS Congruency Theorem

6. AE = CE and BE = DE 6. CPCTC

This is the order provided in your question:

5. ΔABE ≅ ΔCDE 5. AAS Congruency Theorem

3. ∠ABD ≅ ∠CDB 3. Alternate Interior Angles Theorem

1. ABCD is a parallelogram 1. Given

2. AB||DC and AD||BC and AB ≅ DC 2. Definition of parallelogram

6. AE = CE and BE = DE 6. CPCTC

4. ∠DEC ≅ ∠BEA 4. Vertical Angles Theorem