You may wish to use the end-of-chapter summaries to help you organize your ideas. Read the "Work to be done" section below for more specific instructions.

Statements and definitions in the Summaries at the end of each chapter of B&B. Don't ignore the corollaries to Principle 12.

Concurrence of perpendicular bisectors — how it is proved and how it is used to construct the circumcircle.

• One major theme is the geometry of right triangles. You can use similarity to tell a lot about sides and angles of various subtriangles of a right triangle.
• A second theme is the continuing one of the relationship between perpendicular bisectors and distance.

In these proofs you can use the triangle congruence criteria, SAS, SSS, ASA and the basic properties of isosceles triangles stated in Theorems A, B, C of B&B, p. 20-23.

Do these constructions with compass and unmarked straightedge (or ignore the marks). Some basic methods will be explained in class; Chapter 6 of B&B also has information.

Draw a segment. Then use straightedge and compass to construct a square, one of whose sides is the given segment.

Be sure to leave your construction marks showing. Do not use other drawing tools than the compass and straightedge.

Draw an obtuse triangle. Construct (with straightedge and compass the 3 altitudes of this triangle.

What do you observe?

(a) Carry out an example of the construction on B&B, page 189.

(b) Discuss why this works. What is the angle measure of the angle you get?

Be sure to state what you are proving. Be clear about givens, definitions and reasons. You don't have to be pedantic, just make it clear to the reader how the proof works and also that you know what you are talking about.

B&B p. 75, 10-12

B&B p. 101 #9, 10, 11

Use the Web t o find out about the classical Greek problem of trisecting an angle with straightedge and compass. Explain why problem 2.3 does not contradict the impossibility of this construction.