Explanation Given information: Given theorem: If two parallel lines are cut by a transversal, then same side interior angles are supplementary. Calculation: Consider that a ∥ b ; transversal c cuts a and b . ∠ 1 + ∠ 4 = 180 ° Prove that, ∠ 1 is supplementary to ∠ 4 The proof is as follows: Statement Reasons 1. a ∥ b Given 2. ∠ 1 = ∠ 2 Alternate interior angles 3. ∠ 4 + ∠ 2 = 180 ° Angle on a straight line 4. ∠ 1 + ∠ 4 = 180 ° By using 2 and 3 5. ∠ 1 is supplementary to ∠ 4 If the sum of two angle are 180 ° then both angles are supplementary for each other

McDougal Littell Jurgensen Geometry: Student Edition Geometry

5th Edition

ISBN: 9780395977279

Author: Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Publisher: Houghton Mifflin Company College Division

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Question

Chapter 3.2, Problem 22WE

To determine

To write: a proof in two-column form for given theorem.

Expert Solution & Answer

Explanation of Solution

Given information:

Given theorem:

If two parallel lines are cut by a transversal, then same side interior angles are supplementary.

Calculation:

Consider that a∥b ; transversal c cuts a and b . ∠1+∠4=180°

McDougal Littell Jurgensen Geometry: Student Edition Geometry, Chapter 3.2, Problem 22WE

Prove that, ∠1 is supplementary to ∠4

The proof is as follows:

Statement	Reasons
1. a∥b	Given
2. ∠1=∠2	Alternate interior angles
3. ∠4+∠2=180°	Angle on a straight line
4. ∠1+∠4=180°	By using 2 and 3
5. ∠1 is supplementary to ∠4	If the sum of two angle are 180° then both angles are supplementary for each other

Chapter 3.2, Problem 21WE

Chapter 3.2, Problem 23WE

Chapter 3 Solutions

McDougal Littell Jurgensen Geometry: Student Edition Geometry

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