   Chapter 2.3, Problem 33E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 31 to 33, give a formal proof for each theorem.If two lines are each parallel to the same line, then these lines are parallel to each other. (Assume three coplanar lines.)

To determine

To find:

The formal proof for the given theorem.

Explanation

Given:

Two lines w and y are each parallel to the same line x.

Figure (1)

Theorem:

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

Approach:

Line w is parallel to line x.

So,

12

Line y is parallel to line x.

So,

23

Use Transitive Property of congruence.

13

1 and 3 are corresponding congruent angles.

Thus, line w is parallel to y.

The formal proof for the given theorem is shown in the following table,

 Proof Statements Reasons 1. w∥x 1. Given 2. y∥x 2. Given 3. ∠1≅∠2 and ∠2≅∠3 3. If two ∥ lines are cut by a transversal, then the corresponding ∠s are ≅ 4

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

In Exercises 1-4, simplify the expression by factoring. x23x28x7

Calculus: An Applied Approach (MindTap Course List)

x2 2x 5 = 0

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

12. If a line is vertical, then its slope is.

Mathematical Applications for the Management, Life, and Social Sciences

Solve each equation. x4+81=0

Trigonometry (MindTap Course List)

The distance from (1, 2, 1) to the plane 6x + 5y + 8z = 34 is:

Study Guide for Stewart's Multivariable Calculus, 8th 