Thursday, March 13, 2008
Geometry (Class 61)
Announcements
Test Friday. Focus will be on Chapter 8 Lesson 1- Lesson 5.
Lesson Title
A Useful Little Theorem
Overview
In today’s class the warm-up focuses on finding the volume of a very special pyramid, one with a square base and a vertex over one of the vertices of the square. Finding the volume of this solid will lead us to finding a general formula for all pyramids and cones.
During the lesson we finish developing the concepts related to similar right triangles in right triangles, seeing how a table can help us organize the data. We then apply these concepts to proving the Pythagorean Theorem.
Textbook Sections
9.2 (Txt. p.536) The Pythagorean Theorem
Vocabulary
similar, similarity statement
ratio
proportion
scale factor
statement of proportionality
geometric mean
golden section
golden rectangle
altitude
hypotenuse
right triangle
Key Attitudes
Math is about thinking creatively.
Key Ideas
Inside any right triangle there exists other right triangle which are similar to the original.
Since the right triangles created by constructing an altitude to the hypotenuse are similar, the corresponding sides are proportional.
If you are given a geometric mean, you only need two values to solve the proportion.
Since some of the proportions share the length of a side, and that side length is across from itself in the proportion, a geometric mean is created.
Key Skills
Creating similar right triangles inside a right triangle.
Solve problems involving similar right triangles formed by the altitude drawn from the hypotenuse of the right triangle
Creating and using geometric means to solve problems.
Matching corresponding pieces of similar triangles.
Turn-In (#60)
§9.1 (Txt. p.531)#11-21, 25-27
Test Corrections
Handouts
Chapter 8- Lesson 7: A Useful Little Theorem
Assignment
§9.1 (Txt. p.531)#22-24, 27-31, 35
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.
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