Question

If the lengths of the two diagonals are given, which
one of these quadrilaterals can be constructed in a
unique way?
a. Rectangle b. Rhombus
c. Trapezium d. Parallelogram​

Answer 1

Answer:

Rhombus

Step-by-step explanation:

If the two diagonals of a quadrilateral are given, we must know the angle at which they intersect. In a Rhombus , according to its properties, the diagonals will only intersect perpendicularly ( at 90 degrees ). So, we can construct a unique Rhombus if the measurements of the diagonals are given.

Answer 2

If the lengths of the two diagonals are given, a rhombus is the figure which can be constructed in a unique way

The steps for construction of rhombus are:

1. Draw a diagonal AC.

2. Draw a perpendicular bisector of AC, let the perpendicular bisector and AC intersect at O (∵ Diagonals of rhombus intersects at right angle)

3. Taking O as centre and half of the length of another diagonal as radius, mark arc on the perpendicular bisector at both sides of AC. Name these intersection points as B and D

4. Join AB,AD,BC,CD.

5. ABCD is the required rhombus.

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