Question

State whether true or false:

We can construct a rhombus if both its diagonals are known.

• A. True
• B. False

Answer 1

The correct option is A True

The given statement is true.

If we know the side only, we can't construct a unique rhombus because specific angles will be required to construct it,

or

if all angles are given, then also we can't construct a unique rhombus because a side length will be required to construct it.

But if the diagonals of rhombus are given we can construct a complete unique rhombus.

Here are the steps:

1. Draw a diagonal $AC$.

2. Draw a perpendicular bisector of $AC$, let the perpendicular bistro and $AC$ intersects at $O$ ($\because$ 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.