1. Construct the following angles, 30, 45, 60 and 90. Construct an equilateral triangle for 60, bisect one of the angles for 30. Construct a perpendicular.

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Presentation transcript:

1. Construct the following angles, 30, 45, 60 and 90. Construct an equilateral triangle for 60, bisect one of the angles for 30. Construct a perpendicular for 90 and bisect one of the angles for 45. § 5.1

2. Construct an equilateral triangle.

3. Given three segments of 3, 4 and 5 units. Construct a triangle using those three sides.

4. Construct a triangle. Bisect an equilateral triangle.

5. Construct a triangle. Construct a square and bisect it with a diagonal.

6. Construct the incenter (angle bisectors concur) of a triangle. Construct the three angle bisectors. Can you find the radius of the incircle?

7. Construct the circumcenter (perpendicular bisectors concur.) of a triangle. Construct the three perpendicular bisectors. Can you find the radius of the circumcircle?

8. Construct the centroid (medians concur.) of a triangle. Construct the three medians. What is the ratio of the distance from the centroid to the vertex and the distance from the centroid to the midpoint of the side?

9. Construct the orthocenter (altitudes concur.) of a triangle. Construct the three altitudes.

10. Prove that the angle bisector construction works. C A B D