Question

ABCD is a trapezium in which ab is parallel to dc . Diagonals ac and bd intersect each other at o . If ao/oc= bo/od= 1/2 and ab = 4cm .find CD

Answer 1

CD = 8 cm.

Step-by-step explanation:

In the given trapezium, between the triangles Δ AOB and Δ COD has

$\frac{AO}{OC} = \frac{BO}{OD} = \frac{1}{2}$ and ∠ AOB = ∠ COD {As they are vertically opposite angles}

So, the two pairs of corresponding sides of the above two triangles are in the same ratio and their including angles are the same.

Therefore, Δ AOB and Δ COD are similar triangles.

Hence, $\frac{AB}{CD} = \frac{1}{2}$

⇒ CD = 4 × 2 = 8 cm. {Since AB is given to be 4 cm. (Answer)