Question

Construct a parallelogram ABCD whose two diagonals AC = 5.4 cm, BD = 4.8 cm and the acute angle between the diagonals is ${60}^{\circ }$ [4 MARKS]

Answer 1

Concept : 1 Mark
Steps : 1 Mark
Construction : 2 Marks

Concept :
Diagonals of a parallelogram bisect each other. i.e., AO = CO and BO = DO

Steps of Construction:
1. Draw a line segment AC of length 5.4 cm and locate its midpoint O.
2. Construct an angle of ${60}^{\circ }$ as $\angle COX$.
3. Taking the centre as O draw an arc of 2.4cm and mark the intersecting point as D.
4. Similarly, repeat step 2 as $\angle AOY$ on the opposite side.
5. Repeat step 3 and mark it B on the opposite side.
3. Join AB, BC, CD and DA.
4. ABCD is the required parallelogram.