Math Problem Statement

A rhombus with right angles

Solution

A rhombus with right angles is a square. Here's why:

  • A rhombus is a quadrilateral with all sides equal in length.
  • A right angle means the angle measures 9090^\circ.

For a rhombus to have right angles, all four angles must be 9090^\circ. This means the rhombus also satisfies the definition of a square, which is a quadrilateral with all sides equal and all angles 9090^\circ. Hence, a rhombus with right angles is essentially a square.

Would you like further details or have any questions?

Here are five related questions that expand on this topic:

  1. How can you find the area of a square given its side length?
  2. What are the properties of a square in terms of symmetry?
  3. How does the diagonal of a square relate to its side length?
  4. What is the perimeter of a square if one side is given?
  5. How does a square differ from a generic rhombus?

Tip: The diagonals of a square bisect each other at right angles and are equal in length.

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Math Problem Analysis

Mathematical Concepts

Geometry
Quadrilaterals
Properties of a Rhombus
Properties of a Square

Formulas

Area of a square: A = side^2
Perimeter of a square: P = 4 × side

Theorems

Definition of a rhombus
Definition of a square
Properties of right angles

Suitable Grade Level

Grades 6-8