Mathematics

Problem

Quadrilateral

ABCD

has diagonals

AC

and

BD

intersecting at point

O

such that

AO = OC

and

BO = OD

. a. (i) Prove that

\triangle AOB \cong \triangle COD

. b. (ii) Using the result of part (i), show that

AB \parallel CD

and

AD \parallel BC

. c. (iii) Hence, identify the special name of quadrilateral

ABCD

and give a complete justification for your answer.