In □ ABCD , side BC|| side AD. seg AC And seg BD intersect in point Q if AQ =1/3 AC Then show that DQ = 1/2 BQ.
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Step-by-step explanation:
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DQ = BQ/2 in in quadrilateral ABCD side BC|| side AD. seg AC And seg BD intersect in point Q if AQ =1/3 AC
Step-by-step explanation:
side BC|| side AD
seg AC And seg BD intersect in point Q
=> ∠ADQ = ∠CBQ
∠DAQ = ∠BCQ
∠DQA = ∠BQC ( opposite angle)
=> ∠DQA ≈∠BQC
=> DQ/BQ = AQ/CQ
AQ = AC/3
=> AC = 3AQ
CQ = AC - AQ = 3AQ - AQ = 2AQ
=> DQ/BQ = AQ/2AQ
=> DQ/BQ = 1/2
=> DQ = BQ/2
QED
Proved
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