Given ABCD is a parallelagram diagonals AC and BD intersect at E Prove AE is congruent to CE and BE is congruent to DE

Question

Giovani York

Mathematics

6 February, 10:56

Given ABCD is a parallelagram diagonals AC and BD intersect at E Prove AE is congruent to CE and BE is congruent to DE

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Mariela Porter · Answer 1

1. ABCD is a parallelogram - -Given

2. AB≌CD--parallelogram side theorem

3. AB∥CD--def. of parellelogram

4. ∠ABE and ∠CDE are alt. interior angles- - def. of alt. interior angles

5.∠BAE and ∠DCE are alt. interior angles- - def. of alt. interior angles

6. ∠BAE≌∠DCE--alt. interior angles theorem

7. ∠ABE≌CDE--alt. interior angle theorm

8. ⊿BAE≌⊿DCE- - ASA

9. AE≌CE- - CPCTC

10. BE≌DE- - CPCTC