Rhombus
A rhombus is a parallelogram with all four sides of equal length. Its angles are not necessarily 90°, which distinguishes it from a square. A square is a special case of a rhombus where all angles are right angles. In Grade 7 Saxon Math Course 2, Chapter 6, students classify quadrilaterals including the rhombus within the parallelogram family. Recognizing the rhombus and its properties — equal sides, opposite equal angles, and diagonals that bisect each other perpendicularly — is essential for geometry proofs in later courses.
Key Concepts
Property A rhombus is a parallelogram where all four sides have equal length.
Examples A square is a special rhombus with four right angles. A quadrilateral with four sides of length 8 cm is a rhombus.
Explanation Imagine a square that got pushed over. The sides are still equal, but the angles are not necessarily $90^\circ$. It's the classic diamond shape you see on playing cards! It's basically a tilted square, adding a little bit of flair to the quadrilateral world.
Common Questions
What is a rhombus in math?
A rhombus is a quadrilateral with all four sides of equal length. It is a type of parallelogram, so opposite angles are equal and adjacent angles are supplementary.
How is a rhombus different from a square?
Both have four equal sides, but a square also has four right angles. A rhombus can have angles of any measure as long as opposite angles are equal.
Is a square always a rhombus?
Yes. A square has four equal sides, which satisfies the definition of a rhombus. Every square is a rhombus, but not every rhombus is a square.
What are the properties of a rhombus?
A rhombus has four equal sides, opposite angles that are equal, adjacent angles that are supplementary (add to 180°), and diagonals that bisect each other at right angles.
When do 7th graders study the rhombus?
Saxon Math, Course 2, Chapter 6 covers the rhombus as part of the Grade 7 quadrilateral classification and geometry unit.
How do you find the perimeter of a rhombus?
Multiply the length of one side by 4, since all four sides are equal. A rhombus with sides of 7 cm has a perimeter of 4 × 7 = 28 cm.