Prove That In A Parallelogram Opposite Sides Are Equal.
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