### MWF 9

## 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.