Quadrilateral Hierarchy Math Example 3
Follow the full solution, then compare it with the other examples linked below.
Example 3
easyA quadrilateral has all angles equal. What type of quadrilateral is it? What is each angle's measure?
Solution
- 1 Step 1: Interior angles sum to . If all four angles are equal: each angle .
- 2 Step 2: A quadrilateral with four right angles is a rectangle (and if the sides are also equal, a square).
Answer
Each angle is ; the quadrilateral is a rectangle (or square).
The only quadrilateral with all angles equal is one where each angle is 90°, because . A quadrilateral with four right angles must be a rectangle by definition. If, additionally, all sides are equal, it is a square.
About Quadrilateral Hierarchy
The quadrilateral hierarchy organizes four-sided polygons by their properties in a classification tree. Every square is a rectangle, every rectangle is a parallelogram, and every parallelogram is a trapezoid — each level adds constraints like equal sides or right angles.
Learn more about Quadrilateral Hierarchy →More Quadrilateral Hierarchy Examples
Example 1 easy
A quadrilateral has three angles of [formula], [formula], and [formula]. Find the fourth angle.
Example 2 mediumExplain the quadrilateral hierarchy: How is a square related to a rectangle, rhombus, and parallelog
Example 4 hardIn parallelogram [formula], [formula] and [formula]. Find all four angles. Use the property that con