Question

what is the solution​

Answer 1

Answer :

In triangle ADC and triangle CBA

AD = CB

DC = BA (opposite sides of a parallelogram are equal)

AC = CA ( Common )

Therefore , triangle ADC is congruent to triangle CBA by ss congruency rule

Angle ACD = Angle CAB ( By cpct )

Angle CAB = Angle CAD ( Given)

=> Angle ACD = Angle BCA

Thus , AC also bisects angle C

Angle ACD = Angle CAD ( proved )

=> AD = CD ( opposite sides of equal angles of a triangle are equal )

Also , AB = BC = CD = DA ( opposite sides of a parallelogram )

Thus , ABCD is a rhombus