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Question
In the following figure, ∆PQR is right-angled at P. U and T are the points on line QRF. If QP || ST and US || RP, find ∠S.
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Solution
QP || ST and QT is a transversal.
∴ ∠PQT = ∠STQ ...[Alternate interior angles]
US || PR and UR is a transversal.
∴ ∠PRU = ∠SUR ...[Alternate interior angles]
Two angles of ∆PQR equal to two angles of ∆STU.
Therefore, the third angle also will be equal.
∴ ∠QPR = ∠TSU
Now, given that ∠P = 90°
∴ ∠S = 90°.
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