Opposite sides of parallelogram are equal

In this chapter we will prove that ” in parallelogram, opposite sides are equal “.

This is very important property so make sure you remember it for your exam.

opposite sides of parallelogram are equal

ABCD is a parallelogram in which opposite sides are parallel to each other.
AB || CD and AD || CB

To Prove:
Prove that opposite sides are equal in length.
AB = CD and AD = CB

AB & CD are parallel lines intersected by transversal AC.

∠CAB = ∠ACD ( alternate angle )
∠CAD = ∠ACB ( alternate angle )

Now consider triangle ABC and ADC;

∠CAB = ∠ACD ( alternate angle )
AC = CA ( common side )
∠CAD = ∠ACB ( alternate angle )

By ASA congruency, both the triangles are congruent.
So, \mathtt{\triangle ABC\ \cong \triangle ADC}

Since both triangles are congruent, we can say that;
AB = CD and AD = CB

Hence Proved.

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