# Module 4 - Geometry

## Standards

### Understand congruence and similarity using physical models, transparencies, or geometry software.

• 8.G.1. Verify experimentally the properties of rotations, reflections, and translations:
• a. Lines are taken to lines, and line segments to line segments of the same length.
• b. Angles are taken to angles of the same measure.
• c. Parallel lines are taken to parallel lines.
• 8.G.2. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
• 8.G.3. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
• 8.G.4. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
• 8.G.5. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

### Understand and apply the Pythagorean Theorem.

• 8.G.6. Explain a proof of the Pythagorean Theorem and its converse.
• 8.G.7. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
• 8.G.8. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

### Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

• 8.G.9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

### Objectives

1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.

### Lesson 4.05 (Under Construction)

#### References

Florida Educational Technology Clearinghouse. (2009). Flashcard of a Right Triangle Clip Art. Retrieved July 16, 2011, from Florida Educational Technology Clearinghouse: http://etc.usf.edu/clipart/41700/41747/fc_righttri_41747.htm Klinzmann, J. (2009, January 28). Math Made Easy. Retrieved July 17, 2011, from You Tube: Math Made Easy: Using the Pythagorean Theorem Mathsnet. (2011). Interactive Pythagoras's Theorem . Retrieved July 17, 2011, from Mathsnet: http://www.mathsnet.net/dynamic/pythagoras/theorem.html TeacherTubeMath. (2009, August 25). Right Triangles and the Pythagorean Theorem . Retrieved July 17, 2011, from YouTube: http://www.youtube.com/watch?v=fZG_A5AzxIU&NR=1

Grading Summary
A B C D
94-100 80-89 70-79 65-69

### What You Need to be Successful

• Computer - PC or Mac with multimedia capabilitieis.
• Software - Presentation, Word Processing, and Spreadsheet (can be open source).
• Time Management - Deadlines approach quickly - don't wait until the last minute to get the job done!

#### Problem of the Week

In addition to assignments, quizzes and tests, students will develop math skills through the weekly enrichment activity, or Problem of the Week (POW). This problem will be due the last day of each week (normally Thursday). Each POW has four parts - the main problem and three exercises which further develop the strategy introduced in the main problem.

### About Your Instructor Stefanie Brimacomb is a multi-endorsed math, business, and computer teacher in a remote Idaho town where online learning is essential to provide students a competitive education.

Contact Information

e-mail:brimstef@citlink.net
cell/text:(208)413-3783