Construct a rectangle ABCD given AC=6cm and angle between diagonals is $30^{\circ}$ .

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Solution

(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 $¯ X Y$ 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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To construct a rectangle ABCD given AC=6cm and angle between diagonals is $30^{\circ}$ , which of the following properties of rectangles do we use?

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