Question

In the given figure, it is given that AD = BC and AC = BD. Prove that ∠CAD = ∠CBD and ∠ADC = ∠BCD.

Answer 1

Consider the triangles DAC and CBD.

$$\begin{gathered} \begin{array}{r}AD=BC \\ AC=BD\\ DC=DC\end{array} \end{gathered}$$

By SSS criterion of congruence, $∆ADC\cong BCD$.

By CPCT, we have:

$$\begin{gathered} \begin{array}{r}\angle CAD=\angle CBD \\ \angle ADC=\angle BCD\\ \angle ACD=\angle BDC\end{array} \end{gathered}$$

Hence proved.