Question

A parallelogram can be constructed uniquely if both diagonals and the angle between them is given.

Options

• True

• False

Answer 1

This statement is True.

Explanation:

1. Mark a point A and draw a line through A.
2. From A, draw an arc of radius of length equal to one diagonal to cut the above line at C.
3. Bisect AC at O.
4. From A and C, draw arcs of radius more than half the length of AC on both sides, Let they cut at X and Y. XY is the perpendicular bisector of AC. It cuts AC at O.
5. From O, draw a line at the given angle to AC on both sides.
6. From O, draw an arc of radius of half the length of another diagonal on both sides of AC to cut the above line at B and D.
7. Join AB, BC, CD, AD.