Math 150

Fall 2008

Groupwork

Dr. Wilson

9/25 Prove that if two angles in a triangle are congruent, then the triangle is isosceles.

10/2 Prove for Thales of Miletus that the distance from points C to D is the same as the distance from point D to the ship, and prove that point D is the foot of the ship in line AB, along the beach.

10/7 Prove the Isosceles Triangle Theorem

10/9 _Prove the Converse of the Isosceles Triangle Theorem
Prove the Feet in the Mirror problem.

10/14 Prove that a point is equidistant from two given points if and only if it lies on the perpendicular bisector of the line segment between the two points.
Prove that a quadrilateral is a parallelogram if and only if its opposite sides are congruent.

10/16 Prove that a quadrilateral is a parallelogram if and only if the diagonals bisect each other.

10/21 Prove that a four sided figure is a rhombus if and only if the diagonals are perpendicular bisectors of each other.

10/23 Prove that a four sided figure is a rhombus if and only if the diagonals bisect all of the angles.

10/30 Prove that a point lies on the bisector of an angle if and only if it is equidistant from the two sides of the angle.
Prove that the line that goes from a point outside a circle to the center of the circle bisects the angle made by the two tangents from the point to the circle.
Prove that the distances from a point outside a circle to the two points of tangency for the lines which go from the point tangent to the circle are the same.

11/4 Prove the construction for copying an angle.
Prove the construction for bisecting an angle.
Prove the construction for erecting a perpendicular from a point on a line.
Prove the construction for dropping a perpendicular from a point to a line.

11/6 Prove the construction for the perpendicular bisector.

11/18 Fill in all the angles in a regular pentagram.