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Question

State whether true or false:
We can construct a rhombus if both its diagonals are known.

A
True
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B
False
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Solution

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 ( 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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