#5 Perpendicular Bisector and Midpoint

a. Create a circle with radius length AB.[br]b. Place the center of the circle at A.[br]c. Create a circle congruent to the first.[br]d. Place the center of this circle at B.[br]e. Label the intersections of these circles as C and D.[br]f. Create segment CD that is perpendicular to and bisects segment AB.[br]g. Change the color/thickness of your perpendicular bisector.[br]h. Show point M where the two segments intersect.[br]i. Use the angle tool to verify that the segments are perpendicular.[br]j. Use the distance tool to verify that M is the midpoint of segment AB.
Because M is the midpoint of segment AB, it must be centered between these endpoints. Why does the segment connecting C and D pass through the midpoint?
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