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Q9

Expert-verified
Geometry
Found in: Page 34
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

Provide a counterexample to show that each statement is false. You may use words or draw a diagram.

If a line lies in a vertical plane, then the line is vertical.

The counterexample is a wall of the room as a vertical plane, wherein the lines where the wall and the ceiling intercept are horizontal lines, but they still lie in the plane.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1. Define counterexample.

The counterexample is an example for which a hypothesis is true but the conclusion is false for an if-then statement.

Step 2. Observation of the statement.

In order to find a counterexample for the statement “If a line lies in a vertical plane, then the line is vertical.” we need to find a vertical plane wherein a line lies which is not specifically vertical.

Step 3. State the counterexample.

If we look at the wall of the room as a vertical plane, then the lines where the wall and the ceiling intercept are horizontal lines, but they lie in the plane.

Most popular questions for Math Textbooks

State the hypothesis and the conclusion of each conditional.

If , then .

State which definition, postulate, or theorem justifies the statement about the diagram.

If BD¯≅DC¯, then D is the midpoint of BC¯.

Copy everything shown and supply missing statements and reasons.

Given:

m∠1=m∠3;

m∠2=m∠4

Prove: m∠ABC=m∠DEF

Proof:

State which definition, postulate, or theorem justifies the statement about the diagram.

m∠3+m∠4=180

Rewrite each pair of conditionals as a biconditional.

If then is a straight angle. If is a straight angle, then .
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