Construction #3

To erect a perpendicular from a point on a line

Given a point A on a line

scribe two arcs of the same radius centered at A intersecting the line at two points on either side of A.

Call these two points B and C. Open the compass up a little more than it already is and scribe arcs centered at B and C with the same radius.

Call the point where the two arcs meet D. Draw AD.

AD is the line through A perpendiuclar to BC.

Theorem:

Given:

• AB = AC
• BD = CD

To prove:

AD is perpendicular to BC

top