Question

For the figure given below, which of the following is/are correct?

• A. $△ABC\sim △AED$
• B. $\frac{AC}{AD}=\frac{AB}{AE}$
• C. $\frac{AC}{AD}=\frac{BC}{ED}$
• D. $\angle ABC=\angle AED.$

Answer 1

Answer: (A), (B), (C), (D)

$\angle ABC=\angle AED.$

The given figure is as follows:


For $△ABC$ and $△AED,$
$\angle A=\angle A$ (common angle)
$\angle ACB=\angle ADE\left({83}^o\right)$
$\therefore △ABC\sim △AED$ (AA criteria)

So, the corresponding side ratio will be same and third angle will also be equal in measure.

Hence, $\frac{AC}{AD}=\frac{AB}{AE}=\frac{BC}{ED}$
and, $\angle ABC=\angle AED.$

So, all the four options are correct.