Question

prove that opp angles of parallelogram are equal​

Answer 1

Construction: Draw a parallelogram ABCD with AC as diagonal

Prove = angle A = angle C

& angle B = angle D

Proof = Opposite side of parallelogram is parallel then AB||DC & AD||BC

since , AB||DC & AC is transversal

then , angle BAC = angle DCA. ------ (1) ( by alternate interior angles )

similarly ,

AD||BC & AC is transversal

angle DAC = angle BCA -----(2)

Adding eqn 1 & 2 we get ,

angle BAD = angle DCB ( Hence Proved )

Answer 2

To prove that the opposite angles of a parallelogram are equal.

Construction: Draw a parallelogram ABCD. Join BD.

Proof: In triangle ABD and BCD

AB = CD [opposite sides of the parallelogram]

BC = DA [opposite sides of the parallelogram]

BD is common

So triangles ABD and BCD are congruent.

Hence <A = <C , sides opposite BD.

Similarly <B = <D.

Therefore, the opposite angles of a parallelogram are equal.

Proved.