Homework Assignment 1

Due at the beginning of class, Wednesday, 9/27

Read Birkhoff and Beatley (B&B), pp. 20-23.

If a quadrilateral ABCD has AB = DA and BC = CD, we call this quadrilateral a kite. (Compare B&B, page 24, problems #2 and #3, but notice the difference in labeling the vertices.) Construct a kite using your compass. Draw two intersecting circles with centers A and C. Let B and D be the points of intersection. Construct a second example where A and C are on the same side of BD.
State and prove a proposition about a relationship between angles of such a kite. Caution: Does your proof include all cases?
State and prove a proposition about a relationship between the diagonal lines, line AC and line BD, of such a kite. State something more about the relationship between AC and BD than just the angle between them.
Cut out a kite and fold it "in half." How do the properties of a kite you proved above make it possible to fold the kite in this way?
If a quadrilateral ABCD has a four sides equal, we call this quadrilateral a rhombus. State and prove the strongest proposition you can about the diagonals of a rhombus