Question

To construct a rectangle ABCD given AC = 6 cm and angle between diagonals is ${30}^{\circ }$, find the property of the rectangle that will be used to construct the rectangle ABCD.

Answer 1

(1) We draw AC=6cm.
(2) We construct the perpendicular bisector of AC to meet it at O.
(3) At O we construct ${30}^{\circ }$ such that $\overline{XY}$ makes an angle of ${30}^{\circ }$ with AC.
(4) With O as centre and radius 3cm (half of AC= 6cm) We cut arcs in XY at B and D.
(5) Join AB, BC, CD and DA.

So, the properties of the rectangle that are used to construct the rectangle ABCD are, diagonals are equal and diagonals bisect each other.