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