HolcombMath

Thursday, April 23, 2009

Geometry (Class 72)

Lesson Title
Right Triangle Ratios (2)

Overview
The opener for today is focused on working problems in preparation for the CST test. The lesson for the today, continues with working with the relationship between the side lengths and the angle measures of right triangles beginning with students determining the angle measures and missing side length when given the measures of two sides of a right triangle and then reversing the process and finding missing side lengths when the measure of one of the acute angles and one side length of a right triangle are known.
Textbook Sections
§9.5 (Txt. p.558) Trigonometric Ratios

Vocabulary
right triangle
leg
hypotenuse
special right triangle
trigonometry
isosceles right triangle
equilateral triangle
equiangular triangle
45-45-90 triangle
30-60-90 triangle
standard position
reference angle
adjacent side
opposite side
hypotenuse
ratio
trigonometry

Key Attitudes
Math is about building up understanding one idea at a time.

Key Ideas
Certain right triangles are special-- we can figure out the lengths of all three sides when we know the length of only one side.
A 30-60-90 triangle can be created by folding an equilateral triangle.
A 45-45-90 triangle can be created by folding a square.
The fact that the special right triangles are formed either as half of a square or half of an equilateral triangle provides a means to find the length of the other sides when the length of one side is known.
The Pythagorean Theorem can be used to find the length of a missing side of a right triangle when the lengths of two sides are known.
If triangles are similar, then the ratios of corresponding sides are equal.
If you know that two triangles are both right triangles, and you know the measure of one more angle of each of these triangles, then you can determine if the triangles are simialr.
Key Skills
I can find the length of the missing two sides of a 45-45-90 right triangle when I know the length of the remaining side.
I can find the length of the missing two sides of a 30-60-90 right triangle when I know the length of the remaining side.
I can use properties of special right triangles to solve problems.
I can use the ratio of the adjacent side to the hypotenuse of a right triangle to predict the measure of the included angle.
Turn-In (#71)
Txt. p. 328 #54-60, 64
Test Corrections

Handouts
Chapter 9- Lesson 3: Finding Angles
Chapter 9- Lesson 4: Solvign for Angles

Assignment
Finish Chapter 9- Lesson 3
Txt. p. 554 #18-20, 22,23
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.