Assignment 8 (due Wednesday, 11/16)

Reading

Sections 1.1 - 1.2 - 1.3 (all review) and 1.4, 1.5, 1.6, 1.7

Problems to be written up and turned in.

Problems that are referred to by number and section are in Brown, Transformational Geometry.

Problem 8.1 (point symmetry, 5 points)

Write a proof that any point symmetry (also known as a half-turn) is an isometry, showing all cases. (Hint: You can find an outline of how to do this in Problem 15 in Brown, 1.4. But your answer should be comprehensible without looking at the book.)

Problem 8.2 (line x = y, 5 points)

• Write answers to Brown, Section 1.4, #7.

Problem 8.3 (reflections in axes, 5 points)

• Write answers to Brown, Section 1.4, #9.

Problem 8.4 (lines or centers of reflection, 10 points)

• Write answers to Brown, Section 1.4, #11(a), (b) and also an additional (c) P(2,6), P'(4,2).
• Write answers to Brown, Section 1.4, #12.

Problem 8.5 (equilateral triangles on side, 10 points)

• Write answers to Brown, Section 1.7, #5.

Problem 8.6 (double line reflection, 10 points)

• Write proof to Brown, Section 1.7, #12.

Recommended Problems and Reading (not to be turned in)

Some of these are simpler problems that you really should do for practice if you want to be prepared for later work, tests, etc., and some are important problems that were not selected for the written assignment. The simpler ones are mostly short and easy, but they may suggest some new ideas, check on tricky points, etc.

• Section 1.4, read over 1, 3, 4, 5 for some ideas about symmetry.
• Section 1.4, problem 14 was not assigned, but it is very important from lecture.
• Section 1.5, examples 1-4 present methods that will be used in portfolio problems.
• Section 1.6: read the orientation paragraph on page 24 carefully. Also, problem 2 is a coordinate version of a familiar transformation.
• Section 1.7: problems 2, 3, 7, 8.