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Chapter 2: Q13 (page 35)

Provide a counterexample to show that each statement is false.

Statement: If point G is on AB鈫�,then G is onBA鈫�.

Short Answer

Expert verified

The counterexample is the diagram, which shows that the statement is false.

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. State counterexample.

For the given statement 鈥淚f point G is on AB鈫�, then G is on BA鈫�.鈥� let the counterexample by the figure given below:

03

Step 3. Verify the counterexample.

Here, point G is on AB鈫�, because the lineAB鈫� starts with A and then passes through point B and G, but the line AB鈫�is starts from B and passes through A and does not pass through G.

Thus, the line BA鈫� does not pass-through point G.

Therefore, the diagram is a counterexample that shows that the statement is false.

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Most popular questions from this chapter

Can the measure of a complement of an angle ever equal exactly half the measure of a supplement of the angle? Explain.

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I鈥檒l try if you will.
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