Problem 1. Parallelogram
If ABCD is a quadrilateral with AB parallel to CD and with AB = CD, prove that ABCD is a parallelogram.
[You can assume Principles 1 - 16, through the basic theorems about parallel lines. You cannot assume any theorems about parallelograms. Use the standard definition of a parallelogram.]
Problem 2. Constructing external tangents
Given the circle with center O and the point P, construct the lines through P which are tangent to the circle.
Problem 3. External tangent relations
In this figure, the lines PA and PB are tangent to the circle. If we are given that the radius of the circle = r and the distance OP = x, find the distance OQ and show your reasoning. The answer OQ should be an expression involving only r, x and constants. There should be no other distances in the answer.
[In your reasoning, you can use anything you know.]
Problem 4. Constructing a ratio
Given the segment AB on this page, construct the point C on AB so that AC/AB = 5/7.
Problem 5. Perpendicular bisector
Prove: If ABCD is a kite, one of the diagonals is the perpendicular bisector of the other diagonal
[Assume the Basic Principles 1 - 12]
