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Q9.

Expert-verified
Geometry
Found in: Page 216
Geometry

Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279

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Illustration

Short Answer

Write an indirect proof in paragraph form.

Given: Transversal t cuts lines a and b; m∠1≠m<2

Prove: a||b

An indirect proof in paragraph form is-

Proof: Assume temporarily that a is parallel to b, that is., a∥b

If the two lines are parallel, then m∠1 should be equal to m∠2 as alternate exterior angles are equal, however, it is given that role="math" localid="1638446966534" m∠1≠m∠2. Therefore, the assumption a is parallel to b, that is., a∥b is wrong and therefore, a||b.

Hence, a is not parallel to b.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1. Define concept of indirect proof of the statement

An indirect proof is a proof wherein you begin by assuming temporarily that the desired conclusion is not true which then by reasoning logically reaches to a certain contradiction or some other known fact.

Step 2. Steps of writing an indirect proof

1. Assume temporarily that the conclusion is not true.

2. Reason logically until you reach a contradiction.

3. Point out that the assumption was wrong and the conclusion must then be true.

Step 3. State the indirect proof

Consider the following: Transversal t cuts lines a and b; m∠1≠m<2.

In order to write an indirect proof to prove that a||b assume temporarily that the conclusion above is untrue.

Proof: Assume temporarily that a is parallel to b, that is., a∥b.

If the two lines are parallel, then m∠1 should be equal to m∠2 as alternate exterior angles are equal, however, it is given that m∠1≠m∠2. Therefore, the assumption a is parallel to b, that is., a∥b is wrong and therefore, a||b,

Hence, a is not parallel to b.

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