Tuesday, June 03, 2008
Geometry (Class 87)
Lesson Title
Perfecting the Pythagorean Theorem
Overview
The warm-up for today asks students to come up with three methods for finding the diameter of the circumcircle for a triangle. The lesson for today takes us into the last main concept for the year— how to generalize the Pythagorean Theorem so that it works on oblique triangles as well as right triangles.
Textbook Sections
Supplemental
Vocabulary
center
inscribed angle
central angle
radius (pl: radii)
chord
diameter
sections of intersecting chords
extended chords
inscribe
cyclic quadrilateral
law of sines
apothem
oblique triangle
Key Attitudes
Math is about thinking creatively.
Key Ideas
The area of a triangle can be found using the Law of Sines
The Pythagorean Theorem can be “perfected” so that it can be sued with oblique as well as right triangles.
The sum of the two squares is smaller than the area of the third side when the included angle is obtuse and is larger when the included angle is acute.
The amount the Pythagorean Theorem needs to be adjusted can be figured out using right triangle trigonometry.
In order to use the Law of Cosines, you need the measures of two sides and the included angle or the measures of all three sides of a triangle.
Key Skills
I can find the area of a triangle by using the law of sines.
I can explain how why the Pythagorean Theorem needs to be adjusted for oblique triangles.
I can use the Law of Cosines to solve for a missing side of a triangle
I can use the Law of Cosines to solve for an angle in a triangle.
Turn-In (#86)
Benchmark Test 5
Finish Area of Regular Polygon Warm-Up
Finish Chapter 13- Lesson 2: Careful with the Law
Handouts
Chapter 13- Lesson 3: Perfecting the Pythagorean Theorem
Warm-Up: Trigonometry and the Area of Triangles
End of Year Test A Answers
Assignment
Finish Warm-Up
End of Year Test A-- make sure to correct it! You can skip problems 46, 48, 55, 56
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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