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Answers
Answer:
Given : QT = QU and SR || TU
To Find : Prove that
(i) TU = UR.
(ii) RT bisects ∠URS.
Solution:
QT = QU
=> ∠QTU = ∠QUT ( angles opposite to equal sides)
∠PQT = ∠QTU + ∠QUT ( exterior angle of triangle = Sum of opposite interior angles)
=> 8y = 2∠QTU = 2 ∠QUT
=> ∠QTU = ∠QUT = 4y
∠QUT = ∠UTR + ∠URT
=> 4y = 2y + ∠URT
=> ∠URT = 2y
=> ∠UTR = ∠URT
Hence TU = UR
QED
Proved
SR || TU
∠QUT = ∠URS ( corresponding angles)
=> ∠URS = 4y
∠URS = ∠URT + ∠SRT
=> 4y = 2y + ∠SRT
=> ∠SRT = 2y
=> ∠URT = ∠SRT = 2y
Hence RT bisects ∠URS.
QED
Hence proved
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