Mathematics

Problem

In a quadrilateral

ABCD

\angle ABC = 90^\circ

and

\angle ADC = 90^\circ

. It is given that

AB = DC

and

BC = AD

. a. (i) Prove that

\triangle ABC \cong \triangle CDA

. b. (ii) Hence, show that

\angle CAD = \angle DAB

. c. (iii) What special name can be given to the line

AC

with respect to

\angle A

of the quadrilateral? Justify your answer.