Question

In the given figures which of the triangles are similar?

• A. $\Delta DEF\sim \Delta SQR$
• B. $\Delta FED\sim \Delta PQS$
• C. $\Delta EDF\sim \Delta QPS$
• D. $\Delta PQS\sim \Delta QRS$

Answer 1

The correct option is C $\Delta EDF\sim \Delta QPS$

Two triangles are similar if the corresponding angles are equal and the ratio of corresponding sides are the same.
So we need to check which of the angles are equal in the available triangles.

$\angle EDF=\angle SPQ={25}^{\circ }In\Delta QPS,\angle QSP={30}^{\circ }and\angle SPQ={25}^{\circ }$

Since sum of angles in a triangle is ${180}^{\circ }$,
$\angle PQS={180}^{\circ }-{30}^{\circ }-{25}^{\circ }={125}^{\circ }$

Therefore, $\angle DEF=\angle PQS={125}^{\circ }$.

Hence by AA similarity, $\Delta EDF\sim \Delta QPS$