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Congruency of Triangles

In the given ...

Question

In the given figure, if seg PR $≅$ seg PQ, show that seg PS > seg PQ.

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Solution

In △PRS, ∠PRS is an obtuse angle.
Since, a traingle can have maximum one obtuse angle.
Hence, ∠PRS is the greatest angle.
Therefore, the side opposite to ∠PRS i.e., PS is the longest side.
Now, seg PS > seg PR > seg RS
∴ seg PS > seg PQ [∵seg PR $≅$ seg PQ]

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