1. Basic Constructions Constructing Perpendicular Lines
From a point to a line
Perpendicular Bisector

2. Given a line l and a point P not on l, construct a line through P,
perpendicular to line l.
Step 1: Open your compass so that when you place the point of the compass at P the compass extends past line l, and make an arc that intersects line l in two places. Label these points A and B. P l
Put compass point here
Put compass point here
Put compass point here
Step 2: Place the point of your compass at point A and open your compass so that it extends close to B and make an arc below line l. A B C
Step 3: Using the same opening, set your compass at B and make an identical arc, so that it intersects the arc you made in step 2. Label this point C.

3. Given a line l and a point P not on l, construct a line through P,
perpendicular to line l.
Step 4: Draw P A B l C
: The proof of this fact involves the use of congruent triangles.

4. Given a segment, construct its perpendicular bisector.
Step 1: Open your compass so that when you place the point of the compass at A the compass extends more than halfway to B, and make an arc above and below D
Put compass point here
Step 2: Using the same opening, place the point of your compass at point B make a similar arc so that it intersects the arc in step 1 twice. Label the two intersection points C and D. A B
Put compass point here C
Step 3: Draw
: The proof of this fact involves the use of congruent triangles.
and bisects