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As PS||QR, PS || TU
=> angle PTU and angle TPS are interior angles on the same side of the transversal.
=> angle PTU + angle TPS = 180°
=> angle TPS = 180° - 90°
=> angle TPS = 90°
Similarly, angle PSU = 90°
Therefore, PTUS is a rectangle.
=> PT = SU ( opp. sides of a rectangle)
From ∆PTQ and ∆SUR,
angle PTQ = angle SUR = 90° ---- [ Right Angle ]
PQ = SR (given) ---- [ Hypotenuse ]
PT = SU ---- [ Side ]
Therefore, by R H S criterion,
∆PTQ is congruent to ∆SUR
by CPCT,
QT = RU
Hence proved.
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