In the figure below- if the line segment S T is parallel to line segment Q R such that P S-S Q-P T-T R - The provided data is not sufficient to prove that triangles PQR and PST are similar-

The correct option is B False PS SQ = PT TR ...... (given) ST ∥ QR ...... (converse of BPT) Therefore, ∠ PST = ∠ RQR and ∠ PTQ = ∠ PTR Therefore PST ∼ PQR ... ...

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Byju's Answer

Standard IX

Mathematics

Criteria for Similarity of Triangles

In the figure...

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.

True

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False

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Solution

The correct option is B
False

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

$\frac{P S}{S Q}$ = $\frac{P T}{T R}$ and $∠$ PST = $∠$ PRQ. Prove that $Δ$ PQR is an isosceles triangle.

Q. In a triangle PQR, ST is parallel to QR Show that RT(PQ + PS) = SQ (PR + PT)

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

The correct option is B False PSSQ=PTTR ...... (given) ST∥QR ...... (converse of BPT) Therefore, ∠PST=∠RQR and ∠PTQ=∠PTR Therefore △PST∼△PQR ...... (AA similarity) Therefore, the information provided in the question is sufficient to prove that the triangles are similar.

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.