Question

13. The diagonals of a trapezium ABCD intersect at O. AB is parallel to DC, AB = 3 cm and DC = 6 cm. If CO = 4 cm and OB = 3 cm, find AO and DO.​

Answer 1

• AO = 2 cm
• DO = 6 cm

Explanation:

You want the measures of AO and DO in a trapezium in which AB║CD, the diagonals intersect at O, and AB = 3 cm, CD = 6 cm, CO = 4 cm, OB = 3 cm.

Similar triangles

Diagonal AC is a transversal to parallel lines AB and CD, so alternate interior angles BAO and DCO are congruent. Vertical angles AOB and COD are also congruent, so ∆ABO ~ ∆CDO by the AA similarity postulate.

This means the side lengths are proportional, so ...

AB/CD = AO/CO = BO/DO

3/6 = AO/4 = 3/DO ⇒ AO = 2, DO = 6

The measures of AO and DO are 2 cm and 6 cm, respectively.

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Additional comment

It can help to draw a diagram.