Properties of Rhombus
Related Pages
Quadrilaterals
Angles In A Quadrilateral
Polygons
More Geometry Lessons
Math Worksheets
These lessons, with videos, examples and step-by-step solutions, help Geometry students learn about the properties of a rhombus.
A rhombus is a type of quadrilateral (4-sided polygon) with unique characteristics.
The following diagram shows the properties of a rhombus. Scroll down the page for more examples and solutions on using the properties of a rhombus.
What are the Properties of a Rhombus?
A rhombus is a quadrilateral and has all the properties of a quadrilateral
- 4 sides
- 4 vertices
- 4 angles that sum to 360°
A rhombus is a parallelogram and has all the properties of a parallelogram
- 2 sets of opposite parallel sides
- opposite angles are congruent
- consecutive angles sum to 180°
In addition, a rhombus has these special properties
- 4 congruent sides
- diagonals are perpendicular bisectors
- diagonals are angle bisectors
A square is a rhombus with all its angles equal to 90°. Therefore, every square is a rhombus, but not every rhombus is a square.
Symmetry:
- A rhombus has two lines of symmetry, which are its diagonals.
- It has rotational symmetry of order 2 (180°). This means it looks the same after being rotated 180° about the intersection of its diagonals.
Perimeter
The formula for the perimeter of a rhombus is
\( P = 4 \times side \)
Area
The formula for the area of a rhombus is
\(A = base \times height \)
or
\(A = \frac{d_1 \times d_2 }{2} \) (diagonals)
Apply the properties of a rhombus to solve problems
Rhombus Properties
Properties of rhombi often show up in geometric proofs and many other types of problems.
All parallelogram properties apply to rhombus properties since a rhombus is a type of parallelogram.
In a rhombus, there are
- two pairs of parallel sides,
- four sides that are all congruent to each other,
- diagonals that bisect the angles, and
- diagonals that are perpendicular bisectors of each other.
Properties of a Rhombus
A rhombus is a quadrilateral with congruent sides and opposite angles that are congruent.
This video will cover the number of sides of a rhombus, the angles of a rhombus.
In addition, it cover how to find the area of a rhombus and the perimeter.
Properties of a Rhombus
The diagonals of a rhombus are perpendicular and bisect the angles of the rhombus
Area of a Rhombus - Geometry Help
Students learn the formula for the area of a rhombus, and are asked to solve problems using this formula.
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