## Groupwork Assignments

1. 2/21 Prove that a quadrilateral is a parallelogram if and only if the diagonals bisect each other.

2. 2/23 Prove that if one pair of opposite sides in a quadrilateral is both parallel and congruent, then the figure is a parallelogram.

3. 2/26 Prove that a parallelogram is a rectangle if and only if the diagonals are congruent.

4. 3/7 Prove that in a triangle is isosceles if and only if the base angles are congruent.

5. 3/9 1. Prove that if the line from a vertex of a triangle perpendicular to the other side meets the other side at its midpoint, then the triangle is isosceles.

2. Prove that if the bisector of the angle of a triangle is perpendicular to the other side, then the triangle is isosceles.

3. (Extra Credit) If the bisector of an angle of a triangle meets the opposite side at it's midpoint, then the triangle is isosceles.

6. 3/12 Answer the feet in the mirror question. If you are looking at yourself in a mirror and can't quite see down to your feet, should you move closer to the mirror or back away in order to be able to see your feet.

7. 3/14 Prove Thales of Miletus' construction for finding the closest distance from the ship to the shore.

8. 3/16 Prove that if two triangles are congruent, their corresponding altitudes are congruent.

9. 3/19 Prove that a point is equidistant from two given points if and only if it is on the perpendicular bisector of the line segment joining the two points.

10. 3/21 Prove that the distance from a point outside a circle to the two points of tangency are the same.

11. Plrove that the line from a point outside a circle to the center of the circle bisects the angle formed by the two tangents from the point to the circle.

3/23 12. Prove that a point is on the bisector of an angle if and only if its perpendicular distances to both arms of the angle are the same.

3/26 13. Prove the construction for copying an angle.

14. Prove the construction for bisecting an angle.

15. Prove the construction for erecting a perpendicular from a point on a line.

16. Prove the construction for dropping a perpendicular from a point to a line.

17. Prove the construction of the perpendicular bisector of a line segment.

4/27 18. Find the volume and surface area of a regular tetrahedron whose edges are all 1 m. in length.

19. Find the volume and surface area of a regular octahedron whose edges are all 1 m. in length.