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Q9

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Found in: Page 34

### Geometry

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

# 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 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.