Review the Introduction to Math 444 Assignments.
Reading: Chapter 2 of Berele and Goldman
Preparation for Quiz 1 (Friday, 10/11): Be able to prove and use the fundamental theorems about isosceles triangles, kites and equality and inequality of distances. Also, be prepared to construct one of more of the fundamental constructions. More details will be given by Wednesday.
Write proofs for each of the follow problems.
2.1 - Berele-Goldman, Problem 2.2 - Angle sum of convex polygon.
2.2 - Berele-Goldman, Problem 2.3 - Two conditions equivalent to parallelogram definition.
2.3 -Berele-Goldman, Problem 2.4 - Parallelogram is rectangle iff diagonals are congruent.
2.4 -Berele-Goldman, Problem 2.5 - Parallelogram is rhombus iff diagonals are perpendicular to each other.
2.5 - Berele-Goldman, Problem 2.7 - This problem is incorrect as stated. Ignore this problem for Assignment 2. It will be discussed in class.
2.6 - Berele-Goldman, Problem 2.8 - Lines constant distance apart implies alt. interior angles are congruent.
2.7 - Suppose that you take an ordinary ruler. The edges are approximately parallel at a distance d apart. Place the ruler on a sheet of paper and trace a pen or pencil along both edges to draw two parallel lines at distance d apart. Then rotate the ruler and draw two more parallel lines distance d apart. Then the 4 lines intersect in pairs at 4 points. Prove that these 4 points are the vertices of a rhombus.