Question

Diagonals of a quadrilateral ABCD intersect in point O. If 2 QA=QC, 2 OB= OD, then prove that DC= 2AB

Answer 1

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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Answer 2

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