Practice Quadrilateral Hierarchy in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

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 β€” each level adds constraints like equal sides or right angles.

Think of quadrilaterals as a family tree. The most general is any four-sided shape. Add one pair of parallel sides and you get a trapezoid. Add two pairs and you get a parallelogram. Make the angles right and it becomes a rectangle. Make the sides equal and it becomes a rhombus. A square is the 'royal' memberβ€”it has every property: parallel sides, equal sides, and right angles.

Example 1

easy
A quadrilateral has three angles of 85Β°, 95Β°, and 110Β°. Find the fourth angle.

Example 2

medium
Explain the quadrilateral hierarchy: How is a square related to a rectangle, rhombus, and parallelogram?

Example 3

easy
A quadrilateral has all angles equal. What type of quadrilateral is it? What is each angle's measure?

Example 4

hard
In parallelogram ABCD, \angle A = 3x + 15Β° and \angle B = 5x - 5Β°. Find all four angles. Use the property that consecutive angles in a parallelogram are supplementary.