Question

If in $\Delta ABC$ and $\Delta DEF,\frac{AB}{DE}=\frac{BC}{FD},$ then they will be similar if :

• A. $\angle B=\angle E$
• B. $\angle A=\angle D$
• C. $\angle B=\angle D$
• D. $\angle A=\angle F$

Answer 1

The correct option is C $\angle B=\angle D$

In $△ABC$ and $△DEF$

Given $\frac{AB}{DE}=\frac{BC}{FD}$

Now included angle between side $AB$ and $BC$ of $△ABC$ is $\angle B$.

included angle between side $DE$ and $FD$ of $△DEF$ is $\angle D$

So for triangles to be similar $\angle B=\angle D$

Option $C$ is correct.