Class 9 Mathematics Triangles Criteria for Congruence of Triangles

Medium

In the given figure,$PS = QR$ and $PR = QS$. Prove that $(1) \angle PSQ = \angle QRP$ and $(2) \angle SPQ = \angle RQP$.

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Solution

(N/A) In $\Delta SPQ$ and $\Delta RQP$:
$PS = QR$ (Given)
$QS = PR$ (Given)
$PQ = QP$ (Common side)
Therefore,by $SSS$ congruence criterion,$\Delta SPQ \cong \Delta RQP$.
Since the triangles are congruent,their corresponding parts are equal $(CPCT)$.
Thus,$(1) \angle PSQ = \angle QRP$ and $(2) \angle SPQ = \angle RQP$.

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Criteria for Congruence of Triangles

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In the given figure,$PS = QR$ and $PR = QS$. Prove that $(1) \angle PSQ = \angle QRP$ and $(2) \angle SPQ = \angle RQP$.

Similar Questions

Two lines $l$ and $m$ intersect at the point $O$ and $P$ is a point on a line $n$ passing through the point $O$ such that $P$ is equidistant from $l$ and $m$. Prove that $n$ is the bisector of the angle formed by $l$ and $m$.

$l$ and $m$ are two parallel lines intersected by another pair of parallel lines $p$ and $q$ (see Fig). Show that $\Delta ABC \cong \Delta CDA$.

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