Properties of Rhombuses, Rectangles, and Squares
Standard
G.CO.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
Goals for this section:
Rhombuses, rectangles, and squares are all parallelograms that have special properties about them.
Rhombuses
It is a parallelogram with four congruent sides (equilateral).
- Notice that the angles are not equiangular.
Diagonal properties of a Rhombus
Diagonals are perpendicular
If a parallelogram is a rhombus, then the diagonals form a right angle.
Diagonals bisect angles
If a parallelogram is a rhombus, then the diagonals bisect a pair of opposite angles.
- Remember, bisect means to cut in half.
Rectangles
It is a parallelogram with four right angles (equiangular).
- Notice it is not equilateral.
Diagonal Property of a Rectangle
The diagonals of a rectangle are congruent. So AC = BD.
Squares
It is a parallelogram with four right angles and four congruent sides.
Squares have the same properties as parallelograms, rhombuses, and rectangles!
Recall:
Remember that these are all parallelograms so they still have the properties that every parallelogram has! Here's a little summary of the properties:
Rhombuses
- Equilateral
- Diagonals are perpendicular
Additional parallelogram properties:
- Opposite sides are parallel
- Opposite angles are congruent
- Diagonals bisect each other
Rectangles
- Equiangular
- Diagonals are congruent
Additional parallelogram properties:
- Opposite sides are parallel
- Opposite sides are congruent
- Diagonals bisect each other
Squares
- Equilateral and equiangular
- Diagonals are perpendicular and congruent
Additional parallelogram properties:
- Opposite sides are parallel
- Diagonals bisect each other