Practice Quadrilateral Hierarchy in Math

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

Quick Recap

The classification of quadrilaterals based on their properties: parallelogram (two pairs of parallel sides), rectangle (parallelogram with right angles), rhombus (parallelogram with equal sides), square (both rectangle and rhombus), trapezoid (exactly one pair of parallel sides), and kite (two pairs of consecutive equal sides).

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' member—it has every property: parallel sides, equal sides, and right angles.

Example 1

easy
A quadrilateral has three angles of 85°, 95°, and 110°. 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 + 15° and \angle B = 5x - 5°. Find all four angles. Use the property that consecutive angles in a parallelogram are supplementary.
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