Math 150

Fall 2010

Groupwork

Dr. Wilson

1. Prove that if two angles in a triangle are congruent, the sides opposite them are also.

2. Prove the Isosceles Triangle Theorem.

3. Prove the Converse of the Isosceles Triangle Theorem.

4. Thales of Miletus

5. Prove that a point is on the perpendicular bisector of a line segment iff it is equidistant from the endpoints.

6. Given a circle and a point outside the circle, prove that the distances from the given point to the points of tangency, along the tangents to the given circle from the given point, are the same, and that the line from the given point to the center of the circle bisects the angle formed by the tangents from the given point to the given circle.

7. Prove the constructions for

• Copying an angle
• Bisecting an angle
• Erecting a perpendicular from a point on a line
• Dropping a perpendicular from a point to a line
• Constructing the perpendicular bisector of a line segment

8. Prove that a point is on the bisector of an angle iff it is equidistant from the two rays of the angle.

9. Prove

• The opposite sides in a parallelogram are congruent
• If the opposite sides in a quadrilateral are congruent, then it is a parallelogram
• In a parallelogram, the diagonals bisect each other
• If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

10. Prove that if one pair of opposite sides in a quadrilateral is both parallel and congruent, then the figure is a parallelogram

11. Prove that a quadrilateral is a rhombus if and only if the diagonals are perpendicular bisectors of each other.

12. Prove that a quadrilateral is a rhombus if and only if the diagonals bisect the vertex angles.

13. Use Geometer's Sketchpad to construct the 9 point circle.