Homework: Vector proofs in geometry
Use vectors to prove the following:
- Let AB be a chord of circle O, which is not the diameter. Let M be the midpoint of AB. Prove that OM is perpendicular to AB. State this as a theorem about kites.
- Prove that the diagonals of a rectangle are congruent.
- Prove that if the diagonals of a parallelogram are congruent, then it is a rectangle.
- Exercise 4.5.3 in Stillwell (using Figure 4.11).
- Prove Varignon's Theorem: The midpoints of the sides of any quadrilateral form a parallelogram.