Question

Diagonals of a rhombus

1. are equal
2. bisect each other at right angles
3. bisect the angles at the vertices.

Which of the above statements is true?

Options

• only 1

• only 2

• 1 and 2

• 2 and 3

Answer 1

2 and 3

Explanation:

Let’s examine each statement in relation to a rhombus:

1. Diagonals of a rhombus are equal: This statement is false. The diagonals of a rhombus are only equal if the rhombus is also a square. A non-square rhombus has unequal diagonals.
2. Diagonals of a rhombus bisect each other at right angles: This statement is true. By definition, the diagonals of a rhombus are perpendicular bisectors of each other.
3. Diagonals of a rhombus bisect the angles at the vertices: This statement is also true. A diagonal of a rhombus divides each of the two vertex angles it passes through into two equal angles.