After doing this	Your work should look like this
Start with a ray with endpoint A. The right angle will have A as its vertex.
1.  Pick a point not on the given line, about 6 cm from one of its endpoints. Its exact location is not important. Label it D.
2.  Set the compass on point D and set its width to the chosen endpoint .
3.  Draw an arc that crosses the given line and extends over and above the chosen endpoint. (If you prefer, draw a complete circle.)
4.  Draw a diameter through D from the point where the arc crosses the given line.
5.  Draw a line from the chosen endpoint to the endpoint of the diameter line
6.  Done. The last line drawn is perpendicular to the given line.

Explanation of method

• construct a perpendicular at a point on a line or
• construct a perpendicular to a line from an external point

Proof

This construction works by using Thales theorem. It creates a circle where the apex of the desired right angle is a point on a circle. The image below is the final drawing above with the red items added.

Try it yourself

Constructions pages on this site

Lines

• Introduction to constructions
• List of printable constructions worksheets
• Copy a line segment
• Parallel line through a point
• Perpendicular bisector of a line segment
• Perpendicular from a line at a point
• Perpendicular from a line through a point
• Perpendicular from endpoint of a ray
• Divide a segment into n equal parts

Angles

• Bisecting an angle
• Copy an angle
• Construct a 30° angle
• Construct a 45° angle
• Construct a 60° angle
• Construct a 90° angle (right angle)
• Constructing  75°  105°  120°  135°  150° angles and more

Triangles

• Copy a triangle
• Isosceles triangle, given base and side
• Isosceles triangle, given base and altitude
• Equilateral triangle
• Triangle medians
• 30-60-90 triangle, given the hypotenuse
• Triangle, given 3 sides (sss)
• Triangle, given one side and adjacent angles (asa)
• Triangle, given two sides and included angle (sas)
• Incircle of a triangle
• Circumcircle of a triangle

Triangle Centers

• Triangle incenter
• Triangle circumcenter
• Triangle orthocenter
• Triangle centroid

Circles, Arcs and Ellipses

• Finding the center of a circle
• Circle given 3 points
• Tangent at a point on the circle
• Tangents through an external point
• Focus points of a given ellipse

Polygons

• Hexagongiven one side
• Hexagon inscribed in a given circle
• Pentagon inscribed in a given circle

Non-Euclidean constructions

• Construct an ellipse with string and pins
• Find the center of a circle with any right-angled object