More Constructions

Given a line and a point, construct a line through the point that is parallel to the given line.

Start by drawing a line from the point to the given line Start by drawing a line from the point to the given line. Call the point where the lines intersect J.

Second, draw a circle with whatever width you want, centered at J.

Third, draw a circle of the same radius, centered at R.

Set your compass width to the points where the first arc crosses the two lines.

Move your compass to where the upper arc crosses the transversal, and copy the distance you just measured. Call the point where the arcs intersect S.

Draw a line from R to S. This is parallel to the given line.

Given a line and a point, construct a line through the point that is perpendicular to the given line.

You book gives a perpendicular postulate, which says that through any point there is exactly one perpendicular to a given line.

Given a point on a line, construct a perpendicular to the line through the point.

REMEMBER: . Constructing. parallels . Constructing. perpendiculars  REMEMBER:  Constructing parallels  Constructing perpendiculars  Perpendicular postulate