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Chapter 8: Problem 9

Write the definition of a quadrilateral.

Short Answer

Expert verified
A quadrilateral is a four-sided polygon with interior angles that sum up to 360 degrees.

Step by step solution

01

- Understand Basic Shapes

First, understand that a quadrilateral is a type of polygon. Polygons are shapes with straight sides.
02

- Identify Number of Sides

Next, recognize that a quadrilateral specifically has four sides. The word 'quadrilateral' comes from Latin, where 'quadri-' means four and '-lateral' means sides.
03

- Consider the Angles

All interior angles of a quadrilateral must add up to 360 degrees. This property helps differentiate it from other polygons.
04

- Look at Examples

Examples of quadrilaterals include squares, rectangles, trapezoids, and parallelograms. These all have four sides but may vary in the lengths of sides and angles.
05

- Define

Combine all the information: A quadrilateral is a four-sided polygon with interior angles that sum up to 360 degrees.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

polygons definition
Polygons are shapes with straight sides. These shapes are closed, meaning their sides connect to form a bounded area. The sides of polygons are also known as edges, and the points where these sides meet are called vertices. Polygons can have any number of sides. They are named based on the number of sides they have.
For example:
  • A triangle is a three-sided polygon.
  • A pentagon is a five-sided polygon.
  • The key idea is that all polygons must have straight sides that enclose a space.
Understanding polygons helps us categorize various shapes, including circles, which are not polygons because they have curved sides. Remember that a quadrilateral, having four sides, is one type of polygon.
four-sided shapes
Four-sided shapes are specially categorized under polygons and are called quadrilaterals. The term 'quadrilateral' comes from Latin, where 'quadri-' means four and '-lateral' means sides.
There are different types of quadrilaterals, such as:
  • Squares: All sides are equal, and all angles are 90 degrees.
  • Rectangles: Opposite sides are equal, and all angles are 90 degrees.
  • Trapezoids: Only one pair of sides is parallel.
  • Parallelograms: Opposite sides are parallel and equal in length.
Each of these types of quadrilaterals has unique properties, but they all share the common feature of having exactly four sides.
interior angles sum
The sum of the interior angles of a quadrilateral is always 360 degrees. This is a crucial property that distinguishes quadrilaterals from other polygons.
Here's how you can understand it:
The interior angles are the angles inside the shape. If you draw a quadrilateral and measure each angle, then add them together, they will always total 360 degrees.
  • For instance, a square has four right angles, each measuring 90 degrees. Summing these gives you 360 degrees (90 + 90 + 90 + 90 = 360).
  • This property holds true regardless of the shape's specific features, as long as it remains a quadrilateral.
This sum of interior angles as 360 degrees is a defining feature of quadrilaterals and aligns perfectly with their geometrical properties.

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