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Math

QuestionWhat are the steps to bisect line segment AB\mathrm{AB} using a compass and straightedge?

Studdy Solution

STEP 1

Assumptions1. We have a line segment AB. . We have a compass and a straightedge.
3. The compass can be adjusted to any width.
4. The straightedge can draw straight lines.

STEP 2

Place the compass point on point A and stretch the compass width to be greater than half of AB.
Compass point at A, compass width > AB/2\text{Compass point at A, compass width > AB/2}

STEP 3

Draw an arc across the line segment AB using the compass.
Draw arc across AB\text{Draw arc across AB}

STEP 4

Without changing the width of the compass, move the compass point to point B.
Move compass point to B, keep width constant\text{Move compass point to B, keep width constant}

STEP 5

Draw another arc across the line segment AB using the compass. This arc should intersect with the first arc.
Draw second arc across AB, intersecting with first arc\text{Draw second arc across AB, intersecting with first arc}

STEP 6

Using the straightedge, draw a line passing through the point where the two arcs intersect. This line should also pass through line segment AB.
Draw line through intersection of arcs and AB\text{Draw line through intersection of arcs and AB}

STEP 7

The line drawn in step6 bisects the line segment AB, creating two equal segments.
Line bisects AB\text{Line bisects AB}The line drawn bisects the line segment AB.

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