/Geo_Constructions_1

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