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Triangle Inequality

In the given ...

Question

In the given right triangle PQS, if ∠PSQ < ∠QPS, then which of the following is not always true?

A

PQ < PS

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B

QS < PS

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C

QS > PQ

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D

PQ > QS

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Solution

The correct option is D PQ > QS
∠PSQ < ∠QPS (Given)
Since side opposite to the larger angle is longer in a triangle.
∴ PQ < QS
Also, PQR is a right-angled triangle and PS is the hypotenuse.
∴ PS > PQ and PS > QS
Thus, PQ > QS is the only incorrect condition.
Hence, the correct answer is option (d).

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Similar questions

Q. In the right-angled triangle QPR given below, PS is the altitude to the hypotenuse. The figure is followed by three possible inferences.
I.Triangle PQS and Triangle RPS are similar.
II.Triangle PSQ and Triangle RSP are congruent.
III. Triangle PSQ and triangle RPQ are similar.

Q. In the right angled triangle QPR given below PS is the altitude to the hypotenuse The figure is followed by three possible inferences
I Triangle PQS and Triangle RPS are similar
II Triangle PSQ and Triangle RSP are congruent
III Triangle PSQ and Triangle RPQ are similar
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