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# Basic Constructions

Here are a list of elementary constructions that can be carried out with a straightedge and compass. They are arranged roughly in order of difficulty, and if you can do most of these, you can do most standard geometric constructions.

1. Copy a segment. In other words, mark off a segment that exactly matches the length of a given segment on a different straight line.

2. Copy an angle. Given an angle, make another angle of exactly the same size somewhere else.

3. Bisect a segment. This problem was already solved in Section 1

4. Bisect an angle. Given an angle, find a line through the vertex that divides it in half.

5. Construct a line perpendicular to a given line through a point on the given line.

6. Construct a line perpendicular to a given line and passing through a point not on the given line.

7. Given a line and a point not on , construct a new line that passes through and is parallel to .

8. Construct an angle whose size is the sum or difference of two given angles.

9. Given three segments, construct a triangle whose sides have the same lengths as the segments.

10. Construct the perpendicular bisector of a line segment.

11. Given three points, construct the circle that passes through all of them.

12. Given a circle, find its center.

13. Given a triangle , construct the inscribed and circumscribed circles. The inscribed circle is a circle that fits inside the triangle and touches all three edges; the circumscribed circle is outside the triangle except that it touches all three of the vertices of the triangle.

14. Construct angles of , , , , and if you want a challenge, .

15. Construct a regular pentagon. (A regular pentagon is a five sided figure all of whose sides and angles are equal.)

16. Given a point on a circle , construct a line through and tangent to .

17. Given a circle and a point not on , construct a line through and tangent to .

18. Given two circles and , find lines internally and externally tangent to both.

Next: Algebraic Equivalent Up: construct Previous: Some Final Warnings
Zvezdelina Stankova-Frenkel 2000-11-13