Question

multiple choice

question 9

true or false:

a perpendicular bisector is a ray, segment, or line that only needs to bisect the line segment.

a true

b false

Explanation:

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<reasoning>

Analyze the definition of a perpendicular bisector

A perpendicular bisector must satisfy two distinct conditions:

1. It must bisect the given line segment (divide it into two equal halves).
2. It must intersect the segment at a right angle (\(90^\circ\)), meaning it must be perpendicular.

Evaluate the statement

The statement claims that a perpendicular bisector "only needs to bisect the line segment." This is incorrect because it completely omits the requirement of being perpendicular. A line that only bisects a segment is simply a bisector, not a perpendicular bisector.

Determine the correct option

Since the statement is false, the correct choice is option B.
</reasoning>

<answer>
<mcq-option>A true</mcq-option>
<mcq-correct>B false</mcq-correct>
</answer>

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Answer:

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<reasoning>

Analyze the definition of a perpendicular bisector

A perpendicular bisector must satisfy two distinct conditions:

1. It must bisect the given line segment (divide it into two equal halves).
2. It must intersect the segment at a right angle (\(90^\circ\)), meaning it must be perpendicular.

Evaluate the statement

The statement claims that a perpendicular bisector "only needs to bisect the line segment." This is incorrect because it completely omits the requirement of being perpendicular. A line that only bisects a segment is simply a bisector, not a perpendicular bisector.

Determine the correct option

Since the statement is false, the correct choice is option B.
</reasoning>

<answer>
<mcq-option>A true</mcq-option>
<mcq-correct>B false</mcq-correct>
</answer>

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