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Question

To construct a rectangle ABCD given AC=6cm and angle between diagonals is 30, which of the following properties of rectangles do we use?


  1. Diagonals are equal.

  2. Opposite sides are equal.

  3. Diagonals bisect each other.

  4. Diagonals are perpendicular to each other.


Solution

The correct options are
A

Diagonals are equal.


C

Diagonals bisect each other.


(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.

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