Question

which of the following is a perpendicular bisector?

Explanation:

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<reasoning>

Analyze perpendicular bisector requirements

A perpendicular bisector of a line segment must satisfy two conditions:

1. It must be perpendicular to the segment, forming a \(90^\circ\) right angle (indicated by a square right-angle symbol).
2. It must bisect the segment, dividing it into two congruent halves (indicated by matching tick marks on both sides of the intersection point).

Evaluate the given options

• Option A: Shows a right-angle symbol, but the tick marks on the segment are different (one single tick mark and one double tick mark), meaning the segments are not congruent.
• Option B: Shows a right-angle symbol, but has no tick marks indicating that the segment is bisected.
• Option C: Shows matching single tick marks on both halves of the segment, but lacks the right-angle symbol indicating perpendicularity.
• Option D: Shows both the right-angle symbol (perpendicular) and matching single tick marks on both halves of the segment (bisected).

</reasoning>

<answer>
<mcq-option>(A) right angle with unequal tick marks</mcq-option>
<mcq-option>(B) right angle with no tick marks</mcq-option>
<mcq-option>(C) equal tick marks with no right angle</mcq-option>
<mcq-correct>(D) right angle with equal tick marks</mcq-correct>
</answer>

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Answer:

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<reasoning>

Analyze perpendicular bisector requirements

A perpendicular bisector of a line segment must satisfy two conditions:

1. It must be perpendicular to the segment, forming a \(90^\circ\) right angle (indicated by a square right-angle symbol).
2. It must bisect the segment, dividing it into two congruent halves (indicated by matching tick marks on both sides of the intersection point).

Evaluate the given options

• Option A: Shows a right-angle symbol, but the tick marks on the segment are different (one single tick mark and one double tick mark), meaning the segments are not congruent.
• Option B: Shows a right-angle symbol, but has no tick marks indicating that the segment is bisected.
• Option C: Shows matching single tick marks on both halves of the segment, but lacks the right-angle symbol indicating perpendicularity.
• Option D: Shows both the right-angle symbol (perpendicular) and matching single tick marks on both halves of the segment (bisected).

</reasoning>

<answer>
<mcq-option>(A) right angle with unequal tick marks</mcq-option>
<mcq-option>(B) right angle with no tick marks</mcq-option>
<mcq-option>(C) equal tick marks with no right angle</mcq-option>
<mcq-correct>(D) right angle with equal tick marks</mcq-correct>
</answer>

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