Quadrilaterals Study Guide

What is a Quadrilateral?

A quadrilateral is a polygon with four sides, four vertices, and four angles. The sum of the interior angles of a quadrilateral is always 360 degrees.

Types of Quadrilaterals

There are different types of quadrilaterals, including:

• Square: A quadrilateral with four equal sides and four right angles.
• Rectangle: A quadrilateral with four right angles and opposite sides that are equal in length.
• Parallelogram: A quadrilateral with opposite sides that are parallel and equal in length.
• Rhombus: A quadrilateral with four equal sides but not necessarily right angles.
• Trapezoid: A quadrilateral with one pair of parallel sides.
• Kite: A quadrilateral with two distinct pairs of adjacent sides that are equal in length.

Properties of Quadrilaterals

Each type of quadrilateral has its own set of properties, including angle measures, side lengths, and diagonals. Understanding these properties can help in identifying and classifying quadrilaterals.

Classifying Quadrilaterals

Quadrilaterals can be classified based on their properties. For example, a quadrilateral with four right angles is a rectangle, while a quadrilateral with four equal sides is a square. Understanding the properties of each type of quadrilateral is essential for proper classification.

Practice Problems

Here are some practice problems to test your understanding of quadrilaterals:

1. Identify the type of quadrilateral based on the given properties:
   • Opposite sides are parallel and equal in length
   • Four right angles
2. Find the measure of the missing angle in a quadrilateral with angles measuring 80°, 100°, and 120°.
3. Determine if a quadrilateral with side lengths 4 cm, 4 cm, 6 cm, and 6 cm is a parallelogram.

Summary

In summary, quadrilaterals are four-sided polygons with various properties and types. Understanding the properties of different types of quadrilaterals is important for classifying and solving problems involving these shapes.