In the given figure, ST║PQ, U and T are respectively the mid-points of the sides RS and PQ. Prove that RS^2=PR*RU
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Given : ST║PQ, U and T are respectively the mid-points of the sides RS and PQ
To Find : Prove that RS²=PR*RU
Solution:
ST║PQ
=> ΔRST ~ Δ RPQ by AA similarity as ∠S = ∠P and ∠T = Q ( corresponding angles)
=> RS/RP = RT/TQ Eq1
U and T are respectively the mid-points of the sides RS and PQ
=> ΔRUT ~ Δ RSQ
=> RU/RS = RT/TQ Eq2
From Eq1 and Eq2
RS/RP = RU/RS
=> RS² = RP * RU
=> RS² = PR * RU
QED
Hence proved
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your proof is in above pics
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