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

Answer: (C)

$\angle B=\angle D$

If two sides of a triangle are proportional to the corresponding two sides in another triangle, and their included angles are equal, then the two triangles are similar by SAS rule.
If $\frac{AB}{DE}=\frac{BC}{FD}$, then for two triangles ABC and DEF to be similar, the included angle must be equal. In this case, the included angles are $\angle Band\angle D$.