Question

Solve the following question:
(i) Opposite angles of a quadrilateral ABCD are equal. If AB = 4cm, determine CD.

(ii) Diagonals AC and BD of a parallelogram ABCD intersect each other at O. If OA = 3cm and OD = 2cm, determine the lengths of AC and BD.

Answer 1

(i) Given, opposite angles of a quadrilateral are equal. So, ABCD is a parallelogram and we know that in a parallelogram opposite sides are also equal.
CD=AB = 4cm.
(ii) Given, ABCD is a parallelogram OA = 3cm and OD = 2cm
We know that, diagonals of a parallelogram bisect each other.

$\therefore$ Diagonal AC = 2 OA = 6cm $[\because AO=OC]$

And Diagonal BD = 2OD = 4 cm $[\because BO=OD]$

Hence the length of the diagonals AC and BD are 6cm and 4cm, respectively