Question

ABCD is a trapezium in which AB || CD. The diagonals AC and BD intersect at O. Prove that:
(i) ΔAOB and ΔCOD (ii) If OA = 6 cm, OC = 8 cm,
Find:
(a)area (ΔAOB)/area (ΔCOD)
(b)area (ΔAOD)/area (ΔCOD)

Answer 1

We have,
AB || DC
In ΔAOB and ΔCOD
∠AOB = ∠COD [Vertically opposite angles]
∠OAB = ∠OCD [Alternate interior angles]
Then, ΔAOB ~ ΔCOD [By AA similarity]
(a) By area of similar triangle theorem