Question

In $△ABC,\angle ABC=\angle DAC,AB=8cm,AC=4cm,AD=5cm$. Prove that $△ACD$ is similar to $△BCA$

Answer 1

Given that, in $\Delta ABC,\angle ABC=\angle DAC,AB=8cm,AC=4cmandAD=5cm$.

To prove: $\Delta ACD\sim \Delta BCA$

Proof:

In $\Delta ACD$ and $\Delta BCA$,

$\angle ACD=\angle BCA\left[\text{Common angle}\right]$

$\angle ABC=\angle DAC\left[\text{Given}\right]$

Hence, by $AA$ similarity criterion, we can say that,

$\Delta ACD\sim \Delta BCA\left[Henceproved\right]$