Question

prove that opposite side of a parallelogram are equal

Answer 1

consider a parallelogram ABCD

Draw any one diagonal AC

now consider triangle ADC and triangleCBA

we know that opposite sides are parallel in a parallelogram

ABIICD angleACD= angle CAB (alternate interior angles)

ADIIBC angle DAC=angle BCA (alternate interior angles)

AC =AC (common side)

therefore triangle ADC is congruent to triangle CBA ( BY ASA congruency)

this implies that AD=BC,CD=AB (BY CPCT)

hence opposite sides of a parallelogram are equal