Question

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?

• A. Diagonals are equal.
• B. Opposite sides are equal.
• C. Diagonals bisect each other.
• D. Diagonals are perpendicular to each other.

Answer 1

Answer: (A), (C)

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 ${30}^{\circ }$ 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.