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.
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Answer 1

(1) We draw AC=6cm.
(2) We construct the perpendicular bisector of AC to meet it at O. (1 mark)
(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.
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So, the properties of the rectangle that are used to construct the rectangle ABCD are, diagonals are equal and diagonals bisect each other.
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