Question

Prove that a quadrilateral is a parallelogram if it's opposite angle are equal

Answer 1

hey
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given - ABCD is a quadrilateral in which opposite angles are equal that is <A = <C = x
<B = <D = y

to prove - ABCD is a parallelogram

proof
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• we know that sum of all angles of a quadrilateral is 360°

so, x+y+x+y = 360°

2(x+y) = 360°
x+y = 360°/2 = 180°

here x+y = 180° it means AB||CD
as we know two lines are parallel when the sum of consective interior angles is 180°

similarly BC||AD

so we can say that ABCD is a parallelogram

hope helped
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Answer 2

here is your answer OK

To prove a quadrilateral is a parallelogram following conditions should be met:

The opposite sides of the quadrilateral should be parallel.

The sum of any two adjacent interior angles should be 180°.

Diagonals must bisect each other.

If the above three conditions are met, then its a parallelogram.

Hope this helps…