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Problem 577

Construct the perpendicular bisector of a given segment. Bisect a given angle.

Expert verified

To construct the perpendicular bisector of a given segment AB, draw intersecting arcs above and below the segment when the compass is placed on points A and B. Then, join the intersecting points with a straightedge. To bisect a given angle ∠XYZ, draw arcs that intersect angle sides from the vertex, draw intersecting arcs from the new points, and draw a ray from the vertex through the intersection of these arcs. This ray is the angle bisector.

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Chapter 30

Construct the segment of length equal to \(\mathrm{a} \cdot \mathrm{b}\) where a and \(\mathrm{b}\) are the lengths of the segments below. (Unit length is shown below.)

Chapter 30

Construct the mean proportional between two given segments.

Chapter 30

Construct a line perpendicular to a given line through a given point on the given line.

Chapter 30

Divide a given line segment into parts proportional to given line segments.

Chapter 30

Divide any segment into three congruent segments.

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