Construction: Perpendicular Lines

About Geometry Worksheet Activity 2E:  

 

Activity 2E is practice for construction of perpendicular lines through given points either on or not on a given line.

 

Prerequisite Skill: Construct the bisector of an angle Activity 2C.  Name perpendicular lines (Assignment 2.16).

 

How to construct a line perpendicular to a given line at a point on the line:

 

(Do problem 1 by following the steps below.)

 

1.   Place the compass point at the given point (C) on the line.

 

2.   Draw a long arc (at least half of a circle.) that intersects the line (b) on both sides of the point. Mark and label the points at the intersections

     (A and B). 

 

3.   Place the compass point at one point (A) of intersection.

 

4.   Open the compass to more than the distance between the point (A) of intersection and the given point (C).

 

5.   Draw a long arc on one side of the line.

 

6.   Using the same compass opening, place the compass point at the other point (B) of intersection and draw another long arc that intersects

      the other arc.

 

7.   Use a straightedge to draw a line determined by the point (C) on the line and the intersection of the long arcs.  

 

8.   The line is perpendicular to the given line at the given point.