Question

ABCD is a trapezium in which the diagonals are intersecting at point O. Prove OA/OC=OB/OD. Figure essential

Answer 1

In ΔAOB and ΔCOD,

∠AOB = ∠COD.................[Vertically Opposite Angles]

∵AB║CD and AC is the transversal,

∠BAO = ∠DCO.................[Alternate Angles]

∵AB║CD and BD is the transversal,

∠ABO = ∠CDO.................[Alternate Angles]

∴ ΔAOB ≈ ΔCOD.............[AAA Test]

∴ OA/OC = OB/OD..........[C.P.S.T.]

                  - Hence Proved

Answer 2

THE ABOVE ANSWER IS CORRECT DUDE.......