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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 鈥淚f , then B is the midpoint of .鈥� 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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Most popular questions from this chapter

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

If a number is divisible by 4, then it is divisible by 6.

Prove the following statement by filling in the blanks.

If A and B have coordinated a and b, with b>a, and the midpoint M of AB炉 has coordinate x, then prove x=a+b2.

Proof:

Statement

Reasons

1. A, M, and B have coordinated a, x, and b respectively; b>a.

1. ?

2. AM=x鈭�a;MB=b鈭�x

2. ?

3. M is the midpoint of AB炉.

3. ?

4. AM炉鈮�MB炉, orAM=MB

4. ?

5.x鈭�a=b鈭�x

5. ?

6. 2x=?

6. ?

7. x=a+b2

7. ?

Give an example of a false conditional whose converse is true.

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.

If 鈭�A鈮�鈭�B, then m鈭�A=m鈭�B.

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

m鈭�AEB+m鈭�BEF=180
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