Question

Show that, in a parallelogram opposite sides are equal.

Answer 1

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Given a parallelogram ABCD

To prove AB=CD and DA=BC

Join AC

Proof:ABCD is a parallelogram Therefore AB\\DC and AD\\BC

ADIIBC and transversal AC intersects them at A and C

AngleDAC=AngleBCA (alternative interior angles)

ABIIDC and transversal AC intersects them at A and C

Angle BAC=Angle DCA(alternative interior angles)

AC=AC(common side)

By ASA rule

TriangleADC is congruent to triangle CBA

By CPCT

AD=CB and DC=BA

Answer 2

refer to the given attachment...

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