In the figure below, if the line segment ST is parallel to line segment QR. This data is not sufficient to prove that triangles PQR and PST are similar.

True

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False

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Solution

The correct option is B
False

Since $S T ∥ Q R$ , $∠ Q = ∠ P S T a n d ∠ R = ∠ P T S$ , by AA similarity both triangles are similar.

The theorem of similarity states that the two triangles are similar if their corresponding angles are equal and their corresponding sides are in the same ratio. Therefore, the information provided in the question is sufficient to prove that the triangles are similar.

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