Rhombus and Square
Overview
A rhombus is a parallelogram with four congruent sides, perpendicular diagonals, and diagonals that bisect the opposite angles. A square is the most specialized member of the family: it is both a rectangle and a rhombus, so it has every property of a parallelogram, a rectangle, and a rhombus at once. This lesson adds those properties to the family tree and uses them to solve for angles and lengths.
Vocabulary
- Rhombus
- A parallelogram with four congruent sides. Its diagonals are perpendicular and bisect the opposite angles.
- Square
- A parallelogram that is both a rectangle and a rhombus: four congruent sides and four right angles.
- Perpendicular
- Intersecting at right angles. The diagonals of a rhombus are perpendicular, written with the symbol ⊥.
- Angle Bisector
- A ray or segment that divides an angle into two congruent angles. Each diagonal of a rhombus bisects the two opposite angles it connects.
Main Ideas
- A rhombus has all five properties of a parallelogram, plus four congruent sides.
- The diagonals of a rhombus are perpendicular (they intersect at right angles).
- Each diagonal of a rhombus bisects the opposite angles — it splits each angle it touches into two congruent parts.
- The diagonals of a rhombus cut it into four congruent right triangles.
- A square combines both lists: four right angles and congruent diagonals from the rectangle, four congruent sides and perpendicular, angle-bisecting diagonals from the rhombus.
- On the family tree, the square sits below both the rectangle and the rhombus because it inherits the properties of each.
Lesson Notes
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Lesson Video
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Practice Problems
Want More Practice?
Download the practice worksheet for this lesson, work the problems, then check your work with the solutions.