In the figure below, if the line segment ST is parallel to line segment QR such

Question

In the figure below, if the line segment ST is parallel to line segment QR such that $\frac{P S}{S Q} = \frac{P T}{T R}$ . The provided data is not sufficient to prove that triangles PQR and PST are similar.

Options:

A . True

B . False

C . 4.2 cm

D . 0.525 cm

Answer: Option B
:
B

$\frac{P S}{S Q} = \frac{P T}{T R}$ ...... (given)

$S T ∥ Q R$ ...... (converse of BPT)

Therefore, $∠ P S T = ∠ R Q R a n d ∠ P T Q = ∠ P T R$

Therefore $△ P S T \sim △ P Q R$ ...... (AA similarity)

Therefore, the information provided in the question is sufficient to prove that the triangles are similar.

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