Diagonals of rectangle ABCD intersect in point Q if 2 QA=QC, 2QB=QD then prove that DC=2AB
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Answer:
DC = 2 AB if Diagonals of a quadrilateral ABCD intersect in point O. and 2 OA=OC, 2 OB= OD,
Step-by-step explanation:
2OA = OC
2OB = OD
=> 2OA/2OB = OC/OD
=> OA/OB = OC/OD
=> OA/OC = OB/OD
& ∠AOB = ∠COD ( Vertically opposite angles)
Comparing triangle
ΔOAB & ΔOCD
OA/OC = OB/OD
∠AOB = ∠COD
=> ΔOAB ≈ ΔOCD
=> OA/OC = AB/CD
=> 1/2 = AB/CD
=> CD = 2 * AB
=> DC = 2 AB
QED
proved
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hope this would help you
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