Advanced Geometry

Friday, October 1, 2010
Objective: The student will be able to:
Apply ratio of similarity for slope and tangent ratios
Apply various angle theorems to complex diagrams and problems
Connect specific slope ratios to related angles and their complements
Agenda:
I. Practice review.
II. 4-1 through 4-5 : Slope triangles and angles lead to similar triangles.
III. Methods and meanings before 4-6
IV. 4-11 through 4-15 ( methods and meanings)

Opener
1. The above rectangle is divided into four smaller rectangles with areas of 6x, 42, x2 and 7x. The upper left of rectangle is a square, and the area of the lower right rectangle is 42.

a. Find the dimensions of the original ( large) rectangle

b. What would be the area of the original rectangle, if the bottom left rectangle has a perimeter of 50units?

2. A building casts a 168 foot shadow. At the same time 5’10” Casti Nets casts a 11.5’ shadow. How tall is the building? Draw a diagram and show all work.

3. Write the statement: All zephers are dirigibles into an if – then statement, then write the contra-positive and inverse statements
4. Solve or simplify: a. b. :
5. Solve for x and y
Note: Q is the larger triangle.

6. Prove Triangle Q is similar to triangle
7. Find the area and the perimeter.

8. Graph the following lines and find the Area and perimeter of the resulting polygon.