Question

We defined rhombuses as quadrilaterals whose four sides have the same length. But rhombuses have other properties that are not described specifically in that definition. Give two examples of properties that all rhombuses have but that are not described in the definition of rhombus.

Answer 1

Here are two properties that all rhombuses have but are not described in the definition of rhombus:

Diagonals are perpendicular bisectors: In a rhombus, the diagonals (lines connecting opposite corners) are perpendicular to each other and bisect each other. That is, they divide each other into two equal segments. This property is not mentioned in the definition of a rhombus, but it is a consequence of the equal side lengths and symmetry of the figure.

Opposite angles are congruent: In a rhombus, opposite angles (angles at opposite corners) are congruent. This means that if we label the angles A, B, C, and D, then angle A is congruent to angle C, and angle B is congruent to angle D. This property is not mentioned in the definition of a rhombus, but it can be proven using the properties of parallel lines and alternate interior angles.