Question

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
Mark the correct option

• A. I and II are correct
• B. I and III are correct
• C. only II is correct
• D. All three are correct

Answer 1

Answer: (B)

I and III are correct

Let $\angle PQR=\theta$

$⟹\angle PRQ=\angle QPS={90}^{\circ }-\theta$

$⟹\angle SPR={90}^{\circ }-({90}^{\circ }-\theta )=\theta$

Since the corresponding angles of the $△sPQS,RPS$ and $RQP$ are equal. Hence statement (I) and (III) are correct

However, the sides might not be the same. Hence, statement (II) is not correct