Proving the Parallelogram Diagonal Theorem

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Question:

Proving the Parallelogram Diagonal TheoremGiven ABCD is a parralelogam, Diagnals AC and BD intersect at EProve AE is conruent to CE and BE is congruent to DE

Answer:

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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