Question

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Answer 1

Answer:

In triangle DMC and triangle EMB,

MC = MD ( M is the midpoint)

angle CMD = angle BEM (interior alternate angles)

angle DMC = angle EMB (vertically opposite angles)

Therefore, triangle DMC is congruent to triangle EMB (by AAS)

DC = BE (c.p.c.t)

AB = DC (opposite sides of a parallelogram)

AE = AB + BE = DC + DC = 2DC

In triangle AEP and triangle CDP,

angle AEP = angle CDP (interior alternate angles)

angle APE = angle CPD (vertically opposite angles)

Therefore triangle AEP is similar to triangle CDP (by AA similarity rule)

Sides are in proportion,

EP/DP = AE/DC

EP/PD = 2

Therefore, PE = 2 PD

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