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in the diagram of PARALLELOGRAM ABCD, segment BE is perpendicular to segment CED, segment DF is perpendicular to BFC and segment CE is congruent to segment CF.

Prove ABCD is a rhombus.​

in the diagram of PARALLELOGRAM ABCD segment BE is perpendicular to segment CED segment DF is perpendicular to BFC and segment CE is congruent to segment CF Pro class=

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harshapuranik179

Answer:

In parallelogram ABCD

FD is perpendicular to BC

BE is perpendicular to CD

Consider triangle BEC and triangle DFC

FC = EC (Given)

Angle BEC = Angle DFC (=90°)

Angle BCE = Angle DCF (common)

Therefore triangle BEC is congruent to triangle DFC (AAS congruency)

DF = BE (CPCT)

Since the altitudes are equal their bases will also be equal

Therefore BC = DC

Therefore BC = DC = AD = AB

Therefore ABCD is a rhombus

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