Construction of a Perpendicular Line to a Given Line L

Overview

• The objective is to construct a line perpendicular to a given line, L, passing through a specified point on L.
• Two methods are discussed: using a compass and straight edge, and using a set square.

Method 1: Using a Compass and Straight Edge

1. Initial Setup

   • Place the compass on point A (the given point on line L).
   • Draw an arc on either side of point A ensuring the compass width is more than the distance from the arc to point A.

2. Drawing Arcs

   • From each of the arcs made on line L, draw an arc above the line using the same compass width.
   • Repeat on the opposite side for symmetry.

3. Intersection and Joining

   • Mark the point of intersection of the arcs above the line.
   • Using a straight edge, draw a line from this intersection point to point A.
   • The line drawn is perpendicular to line L passing through point A.

Method 2: Using a Set Square

1. Setup

   • Place the set square on line L at the point A.

2. Drawing the Perpendicular

   • Use the set square to draw a line at a right angle (90 degrees) from point A.
   • The line drawn will be perpendicular to line L passing through point A.

Practice

• Try both methods to reinforce understanding.
• Future lessons will expand on these techniques.