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Chapter 2: Q8 (page 34)

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

If , then B is the midpoint of .

Short Answer

Expert verified

The counterexample is the Equilateral triangle.

Step by step solution

01

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.

02

Step 2. Observation of the statement.

In order to find a counterexample for the statement “If , then B is the midpoint of .” we need to find two lines and such that they are equal to each other but B is not the midpoint .

03

Step 3. State the counterexample.

The equilateral triangle is the counterexample.

In, equilateral triangle line segment and are congruent but point B is not in , so it cannot be its midpoint.

Therefore, the counterexample is an Equilateral triangle.

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