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AlexFokin [52]
3 years ago
6

Proving the Parallelogram Diagonal Theorem

Mathematics
2 answers:
zhannawk [14.2K]3 years ago
5 0

Answer:

Step-by-step explanation:

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

lora16 [44]3 years ago
3 0

Answer:

The proof is given below.

Step-by-step explanation:

Given a parallelogram ABCD. Diagonals AC and BD intersect at E. We have to prove that AE is congruent to CE and BE is congruent to DE i.e diagonals of parallelogram bisect each other.

In ΔACD and ΔBEC

AD=BC              (∵Opposite sides of parallelogram are equal)

∠DAC=∠BCE       (∵Alternate angles)

∠ADC=∠CBE        (∵Alternate angles)

By ASA rule, ΔACD≅ΔBEC

By CPCT(Corresponding Parts of Congruent triangles)

AE=EC and DE=EB

Hence, AE is conruent to CE and BE is congruent to DE


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