Mathematics

Problem

Quadrilateral

ABCD

is a kite in which

AB = AD

and

CB = CD

. Its diagonals

AC

and

BD

intersect at

O

. Answer the following questions. a. Prove that

\triangle ABO \cong \triangle ADO

. Provide clear reasons for each congruence step. b. Using the result of part (i), show that

AO

bisects

\angle BAD

. c. If

\angle BAD = 72^{\circ}

, calculate

\angle BAO

and

\angle DAO

. Give reasons for your answer.