1.6 and 3.6 Constructions By Brit Caswell

Copying A Segment Draw line segment. Draw a ray. Open the compass to length of line segment. Keep your compass open to the same angle and make an arc with the compass point on the endpoint of the ray.

Copying An Angle Draw an arbitrary angle, A. Draw a ray with endpoint S. Draw an arc that intersects both sides of the angle and label these points B and C. With the compass at the same measure, copy that arc on the ray with the intersection labeled R. Open the compass to the width of BC. Put the compass point on R and make an arc through the arc made from R. Label the point of intersection T. Draw ST.

Constructing a Perpendicular Bisector Draw line segment. Open the compass to wider than ½ the length of the line segment and draw two long arcs with that same compass measure, one from each endpoint of the segment. Draw a line segment between the two points of intersection of these arcs. You can always draw a perpendicular line where you’d like on a segment by marking the point on the segment and then marking two points equidistant from the initial point.

Perpendicular from a Point to a Line Draw line r with point M not on the line. With compass point on r, draw an arc that intersects point M in two points, F and Q. Draw two small arcs at F and Q on the opposite side of line r from M. Draw a line segment from the intersection of those two arcs to point M.

Constructing the Angle Bisector Draw angle A. Put the compass point on A and create an arc with intersects both sides of the angle at B and C. Put the compass point on B and draw an arc. Keep the compass at the same width and draw an intersecting arc from point C. Label the intersections of the two new arcs as D. Draw AD.

Constructing Parallel Lines Draw line l and point N. Label two points on l, H and J. Draw HN. Draw an arc at H and copy it at N. Measure the distance using the compass of the arc at H and copy that distance with the arc at N. Draw line m through N and the point of intersection of the arc at N.

Constructing an Equilateral Triangle Draw line p and N on the line. Construct a long arc from point N that intersects p at point R. Keeping your compass the same distance, at R, draw another arc that intersects the original arc. (This arc should also intersect p at N.) Label the intersection of the two arcs E. Draw NE and RE. This construction is not in your book.

Constructing a 30-60-90 Right Triangle Construct an equilateral triangle, making sure that the two arcs intersect on both sides of the line. Draw the line segment through the intersection points. Draw the other side of the triangle as normal. This construction is not in your book.

Constructing a Square Draw line f. Construct perpendicular lines d and y and mark their intersections with f as D and Y. Using your compass, make two arcs from D and Y, which are the length DY. Draw the remaining segment from the intersections with the two parallel lines. This construction is not in your book.

Regular Hexagon Inscribed in a Circle Draw line segment AF. With compass point on A, set its width to AF. Make an arc. Repeat with F, with the arc intersecting the original arc. The intersection of these arcs will be the center of the figure. Mark it as O. Move the compass to O and make a full circle. Move the compass back to A and mark the point for the new vertex. Use the new point to draw the next vertex until you have all six. Draw a line between each vertex. This construction is not in your book.