Assignments for Week 7

This week we will take up a different way of looking at geometry using transformations. However, we will not abandon the approach we have been using (called the synthetic approach) and will be continuing to learn and practice in that domain as well.

You will get an additional (free) textbook this week. It consists of Chapters 5-6 from High School Geometry from an Advanced Standpoint (HSGAS). Some of the reading and problems will be from this book and some from Brown.

Reading

Read Brown, Chapter 1 and HSGAS, Chapters 6.1 and 6.2.

Assignment for Wednesday (CA coming)

In class Monday, the concept of isometry will be defined, with some problem-solving and examples in class. At the beginning of class Wednesday, you will be asked to answer a question of the kind of HSGAS, 6.1.2, Problems 3, 4 or Brown, 1.2, Problems 5, 6, 7, 8.

Assignment 7 (50 points, Due Monday, 11/13)

7.1 Line Reflections are Isometries (10 points)

HSGAS, 6.2.3 Problem 1.

7.2 Isometries Preserve Angle Measure (10 points)

Prove that isometries preserve angle measure. This is an example of a rather generally worded statement. First reword the statement to tell exactly what it means in a form that can be proved. Then prove it.

7.3 Formula for 90-degree rotation (5 points)

HSGAS, 6.2.3 Problem 3.

7.4 Formula of lines in double reflections (10 points)

HSGAS, 6.2.3 Problem 5.

7.5 Barber shop (5 points)

HSGAS, 6.2.3 Problem 6.

7.6 Composition of line reflections (10 points)

HSGAS, 6.2.3 Problem 7.