/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 11 State the characteristics of eac... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 11

State the characteristics of each quadrilateral. Trapezoid

Short Answer

Expert verified
A trapezoid has one pair of parallel sides, non-parallel legs, and the adjacent angles to each base are supplementary. An isosceles trapezoid has equal legs and base angles.

Step by step solution

01

Definition of a Trapezoid

A trapezoid is a quadrilateral with at least one pair of parallel sides. These parallel sides are called the bases of the trapezoid.
02

Non-parallel Sides

The other two sides of a trapezoid are called the legs. These sides are not parallel.
03

Angles of a Trapezoid

The angles adjacent to each base are supplementary, meaning they add up to 180 degrees.
04

Special Types of Trapezoids

An isosceles trapezoid has legs that are equal in length, and the base angles are also equal.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

quadrilateral
A quadrilateral is a four-sided polygon. Some common examples of quadrilaterals include squares, rectangles, and trapezoids. To easily remember, think of a box or a piece of paper, which has four sides.
Each quadrilateral has four vertices (corners) and the sum of its internal angles is always 360 degrees.
  • Examples: If each angle of a quadrilateral is 90 degrees, it is a rectangle or a square.
As we delve into different types of quadrilaterals, it's important to note that their side lengths and angles will vary, but they will always retain four sides.
parallel sides
Parallel sides are sides that run in the same direction and never intersect. In a trapezoid, at least one pair of sides will always be parallel, which are known as the bases.
Imagine railroad tracks; they represent parallel sides because they are always the same distance apart and never meet.
The other two non-parallel sides in a trapezoid are called the legs. They can be of different lengths and are not aligned.
  • In an isosceles trapezoid, the legs are equal in length, making it symmetrical.
This characteristic of having parallel sides is what sets a trapezoid apart from other quadrilaterals.
supplementary angles
Supplementary angles are two angles that add up to 180 degrees. This concept is crucial for understanding the angles in a trapezoid.
In a trapezoid, the angles adjacent to each of the parallel sides (bases) are supplementary. To put it simply, if you pick one angle at the base of a trapezoid, the angle next to it and along the same base will add up to 180 degrees.
For example, if one angle is 70 degrees, the angle next to it along the same base will be 110 degrees.
  • In an isosceles trapezoid, each pair of base angles are equal, showing the concept of supplementary angles perfectly.
Understanding supplementary angles helps in identifying and calculating the angles within different quadrilaterals, especially trapezoids.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The measure of an angle is given. Find the measure of the supplement. $$179^{\circ}$$

In the U.S. Customary System of measurement, 1 ton \(=2000\) Ib. In the metric system, 1 metric ton \(=1000 \mathrm{kg}\). Use this information to answer Exercises \(69-72\). The mass of a Mini-Cooper is 1.25 metric tons. How many pounds is this? Round to the nearest pound.

Find the length of the unknown side. Round to three decimal places if necessary. Leg \(=15 \mathrm{ft}\), hypotenuse \(=18 \mathrm{ft}\)

A can of paint weighs 2lb 4 oz. How much would 6 cans weigh?

Determine the surface area of the object described. Use 3.14 for \(\pi\) when necessary. A cylinder with radius 9 in. and height 15 in.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.