Question

to prove that in a parallelogram opposite angles are equal.

Answer 1

in parallelogram ABCD , we know that AB||CD and DA||CB (parallelogram PPTY.)

Construct diagonal AC,

then angle BAC = ACD (Alternate interior angles are equal) - (1)

angle DAC = CBA (Alternate interior angles are equal) - (2)

by adding LHS and RHS of (1) and (2) we get,

angle BAD = DCB or angle A = C

where A and C are opposite angles

Answer 2

In parallelogram ABCD , we know that AB||CD and DA||CB Construct diagonal AC, angle BAC = ACD -(1) angle DAC = CBA -(2) adding LHS and RHS of (1) and (2) we get, angle A = C where A and C are opposite angles