Question

The diagonals of a trapezium ABCD intersect at O. AB is parallel to DC. AB= 3cm and DC =6cm. If CO= 4cm and OB=3cm. Find AO and DO. (please answer with a diagram)

Answer 1

So from the diagram you must understand tha ratio oa/od = ob/od

So we get that oa/4 = 3/od from the given values

So OA = 3 and OD = 4

As the ratio are equal to each other

Answer 2

Given:

AB= 3cm, DC =6cm, CO= 4cm and OB=3cm

To find:

AO and DO.

Solution:

1) ABCD is the trapezium where the diagonals intersects at O.

2) We will do this question by using the property of the similarity of the triangle.

• In ΔAOB & ΔCOD

• ∠1 = ∠5 (alternate interior angle)

• ∠2 = ∠4 (vertically opposite angle)

• ∠3 =∠6 (alternate interior angle)

so the triangles are similar by the AA similarity rule.

3) Apply the rule of similarity to find the ratios of the sides of the triangle.

• $\frac{3}{6}= \frac{y}{4} =\frac{3}{x}$

Compare the ratios one by one

• $\frac{3}{6}= \frac{y}{4}$

we get the value of y = 2 cm.

• $\frac{3}{6}=\frac{3}{x}$

here we get the value x = 6 cm.

AO = 2 cm and DO = 6 cm.