Geometry Constructions with compass and straightedge a
1. Construct a, a + b, 2b - a
2. Construct a line perpendicular to
b
.
A
3. Construct a perpendicular bisector of
B
.
A
B
4. Construct a line perpendicular to line m through point P.
P
m
5. Bisect angle 3. 3
6. Construct an angle congruent to
.
A
B C
7. Construct a 45˚ angle.! !
!
!
8. Construct a 60˚ angle.
9. Construct a 15˚ angle.! !
!
!
10. Construct a 22.5˚ angle.
A 11. Construct a line parallel to
.
B
12. Circumscribe a circle about the triangle.
13. Inscribe a circle in the triangle.
14. Construct a triangle congruent to
using SSS.
A
C B
15. Construct a tangent to circle P at point Q.
Q
P
16. Construct the tangents to circle P from point R.
R
P
17. Subdivide
into three congruent parts. D C
18. Subdivide parts.
into four congruent
G
H
a 19. Construct a parallelogram with sides a and b.
b
a 20. Construct a square with side length a.
21. Construct an equilateral triangle.
a 22. Construct a rectangle with sides a and b.
23. Construct a rhombus with a 60Ëš angle and side length c. c
b
24. Construct
25. Construct
1
.
.
a b
A
26. Locate the centroid of (the gravitational center) (use the medians)
.
C
B
A
27. Locate the incenter of (use the angle bisectors)
.
C
A
28. Locate the circumcenter of . (use the perpendicular bisectors)
C
A
B
29. Locate the orthocenter of . (use the altitudes of the triangle)
C
B
30. Trisect an arbitrary angle