   Chapter 10.4, Problem 2E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
1 views

# In Exercises 1 to 17, complete an analytic proof for each theorem.The opposite sides of a parallelogram are equal in length.

To determine

The analytic proof for the given theorem “The opposite sides of a parallelogram are equal in length”.

Explanation

Given theorem is,

The opposite sides of a parallelogram are equal in length.

The above graph shows the parallelogram ABCD.

From the theorem the length of the opposite sides of the parallelogram are equal and expressed as below,

Opposite side of AB is CD.

And the opposite side of AD is BC.

The coordinates of the figure are A0, 0, Ba,0, Ca+b, c and D(b, c).

In order to prove “The opposite sides of a parallelogram are equal in length”, needed to use distance formula.

Length of AB= length of CD.

Using distance formula for finding length of the diagonal AC.

Where, A0, 0 and Ba,0

AB=(a-0)2+(0-0)2

Simplifying the above equation,

AB=(a)2

AB=a

Similarly, Ca+b, c and D(b, c)

CD=b-a+b2+(c-c)2

Simplifying the above equation,

CD=(b-a-b)2+(0)2

CD=(-a)2=a2

CD=a

Hence, AB=CD is proved

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find the mean for the following set of scores: 2, 7, 9, 4, 5, 3, 0, 6

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

#### [Type text] 3. If and, does? [Type text]

Mathematical Applications for the Management, Life, and Social Sciences

#### Find the area of the shaded region. 8.

Single Variable Calculus: Early Transcendentals

#### limx5x225x29x+20= a) 1 b) 10 c) d) does not exist

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 