In the adjoining figure, $SP$ and $RQ$ are perpendiculars on the same line $PQ$. Prove that $\Delta P Q S \cong \Delta Q P R$.
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Given :

In the given figure, $SP$ and $RQ$ are perpendiculars on the same line $PQ$. 

To do :

We have to prove that, $\Delta P Q S \cong \Delta Q P R$.

Solution :

$SP = RQ = 5 cm$

$∠SPQ = ∠RQP = 90°$

In $△SPQ$ and $△RQP$,

$PS = RQ = 5 cm$

$∠SPQ = ∠RQP$

$PQ = PQ$ (Common side)

Therefore, by SAS congruency

$\Delta P Q S \cong \Delta Q P R$

Hence Proved.

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Updated on: 10-Oct-2022

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