Question

In the figure, ray $AZ$ bisects $\angle DAB$ as well as $\angle DCB$
(i) State the three pairs of equal parts in triangles $BAC$ and $DAC$.
(ii) Is $△BAC\cong △DAC$? Give reasons
(iii) Is $AB=AD$? Justify your answer
(iv) Is $CD=CB$? Give reasons.

Answer 1

(i)

$\begin{array}{c}\angle DAC=\angle BAC\\ \angle DCA=\angle BCA\\ AC=AC\end{array}$

(ii)

By ASA criterion, triangles are congruent.

(iii)

Since triangles are congruent hence, $AB=AD$ because both sides originate from equal angles in two triangles.

(iv)

Since triangles are congruent hence,$CD=CB$ because both sides originate from equal angles in two triangles.