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In the figure (3) given below, ∠ PQR = ∠ PRS. Prove that triangles PQR and PRS are similar. If PR = 8 cm, PS = 4 cm, calculate PQ.

In the figure (3) given below, ∠ PQR = ∠ PRS. Prove that triangles PQR and PRS are similar. If PR = 8 cm, PS = 4 cm, calculate PQ. Similarity, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

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Answer

Given, ∠ PQR = ∠ PRS.

∠ P = ∠ P (common for both the triangles).

By AA rule of similarity, △PQR ~ △PRS.

Then,

PQPR=PRPS=QRSRConsidering, PQPR=PRPSPQ8=84PQ=644PQ=16.\dfrac{PQ}{PR} = \dfrac{PR}{PS} = \dfrac{QR}{SR} \\[1em] \text{Considering, } \dfrac{PQ}{PR} = \dfrac{PR}{PS} \\[1em] \dfrac{PQ}{8} = \dfrac{8}{4} \\[1em] PQ = \dfrac{64}{4} \\[1em] PQ = 16.

Hence, the length of PQ = 16 cm.

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