Question

show that opposite angles of a parallelogram are equal​

Answer 1

given, PQRS is a parallelogram

to prove: angle P = angle R

opposite sides of parallelogram is parallel SO, AB||DC and AD||BC

since AB||DC

and AC is the transversal

angle BAC= angle DCA (alternate angles)...........(1)

since AD||BC

and AC is the transversal

angle DAC=angle BCA (alternate angles)........(2)

adding 1 and 2

angle BAC+angle DAC=angle DCA+angle BCA

angle BAD=angle DCB

hence proved