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In the adjoining figure, ∠1 = ∠2 and ∠3 = ∠4. Show that PT × QR = PR × ST.

In the adjoining figure, ∠1 = ∠2 and ∠3 = ∠4. Show that PT × QR = PR × ST. Similarity, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

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Answer

Given, ∠1 = ∠2

Adding ∠QPT to both the sides,

∠1 + ∠QPT = ∠2 + ∠QPT

∴ ∠SPT = ∠QPR

∠PST = ∠PQR (As ∠3 = ∠4)

Hence, by AA axiom △PQR ~ △PST.

Since, triangles are similar so ratio of their corresponding sides will be equal.

⇒PTPR=STQR⇒PT×QR=PR×ST.\Rightarrow \dfrac{PT}{PR} = \dfrac{ST}{QR} \\[1em] \Rightarrow PT \times QR = PR \times ST.

Hence, proved that PT × QR = PR × ST.

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