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

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