In the figure given below- if the line segment ST is parallel to line segment QR such that PS - SQ - PT - TR- This provided data is not sufficient to prove that triangles P QR and P ST are similar-A- FalseB- True

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SAS Similarity

In the figure...

Question

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

True

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False

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Solution

The correct option is B
False

In $△ P Q R$ and $△ P S T$ ,

$∠ P S T = ∠ P Q R$ [Corresponding angles]

$∠ P T S = ∠ P R Q$ [Corresponding angles]

$∠ P$ is common.

Thus, 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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Similar questions

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

Q. In given figure,

\frac{P S}{S Q} = \frac{P T}{T R}

and

∠ P S T = ∠ P R Q

. Prove that

△ P Q R

is an isosceles triangle.

In the figure shown below, $\frac{P S}{S Q} = \frac{P T}{T R}$ and $∠ P S T = ∠ P R Q .$ Then $△ P Q R$ is __ triangle.

In below shown figure, $\frac{P S}{S Q}$ = $\frac{P T}{T R}$ and $∠$ PST= $∠$ PRQ. Then $Δ$ PQR is an isosceles Triangle.

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

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