Construction of a Rectangle When Two Adjacent Sides Are Given.
To construct ...
Question
To construct a rectangle ABCD given AC = 6 cm and angle between diagonals is 30∘, find the property of the rectangle that will be used to construct the rectangle ABCD.
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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∘ such that ¯XY makes an angle of 30∘ 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.