Question

Question

Use the image to answer the question.

Two semicircles pass through a horizontal line segment. A vertical line segment connects the two points above and below the horizontal line segment where the semicircles intersect.

Based on the construction marks, what do you know about KO¯¯¯¯¯¯¯¯
and OL¯¯¯¯¯¯¯
?

(1 point)
Responses

KO¯¯¯¯¯¯¯¯=OL¯¯¯¯¯¯¯
Modifying above upper K upper O with bar equals Modifying above upper O upper L with bar

MN¯¯¯¯¯¯¯¯¯¯=KO¯¯¯¯¯¯¯¯+OL¯¯¯¯¯¯¯
Modifying above upper M upper N with bar equals Modifying above upper K upper O with bar plus Modifying above upper O upper L with bar

KO¯¯¯¯¯¯¯¯+OL¯¯¯¯¯¯¯=MN¯¯¯¯¯¯¯¯¯¯
Modifying above upper K upper O with bar plus Modifying above upper O upper L with bar equals Modifying above upper M upper N with bar

MO¯¯¯¯¯¯¯¯¯=KO¯¯¯¯¯¯¯¯+OL¯¯¯¯¯¯¯
Modifying above upper M upper O with bar equals Modifying above upper K upper O with bar plus Modifying above upper O upper L with bar
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Answer 1

Based on the given information about the semicircles and the line segments, it can be inferred that the vertical line segment connecting the two points where the semicircles intersect is a common height for both points of intersection above and below the horizontal line segment.

Since both semicircles are symmetrical about the horizontal line segment, we can conclude that the lengths of the segments KO and OL are equal due to symmetry.

Thus, the correct response is:

KO¯¯¯¯¯¯¯¯=OL¯¯¯¯¯¯¯

This means that the length of segments KO and OL is the same.