/PAP_Geo_Constructions_Log1

PAP Geometry Constructions with compass and straightedge JLister, F107 a

b

1. Construct a, a + b, 2b - a

2. Construct a line perpendicular to

.

A

3. Construct a perpendicular bisector of

B

.

A

B

4. Construct a line perpendicular to line m through point P. P

m

3

5. Bisect angle 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 B

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. Construct a square with an area of five (5) square units.

1

31. Trisect an arbitrary angle.

32. Given

with a radius length of 1 unit, construct a square with the same area.

P