Question

therom

If each pair of opposite sides of a
quadrilateral is equal then it is a parrologram


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Answer 1

Given:-

A quadilateral ABCD

with AB= DC

BC = AD

To prove :-

Quadilateral ABCD is a Parallelogram

Construction:-

Join AC

Proff :-

In triangle ABC and CDA

AB = CD ( Given)

BC = AD ( Given)

AC = AC (Common )

By SSS Congrency

Triangle ABC is congrent to Triangle CDA

Angle 1 = Angle 2 ( C.P.C.T)

But this is a pair of alternate interior angles and when alternate interior angles are equal then lines are parallel

Therefore AB parallel to DC

ALSO ,

Angle 3= Angle 4 ( C.P.C.T)

But this is a pair of alternate interior angles and when alternate interior angles are equal then lines are parallel

Therefore BC parallel to AD

Both pairs of opposite sides are parallel

Therefore quadilateral ABCD is a Parallelogram

Note:-

Figure in attachment

know more about quadilateral :-

IN A QUADILATERAL THERE ARE

4 pairs of adjacent side

2 pairs of opposite sides

2 pairs of opposite angles

4 pairs of adjacent angles

2 diagonals

Answer 2

Step-by-step explanation:

here u goo

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