Name: Period GL UNIT 5: SIMILARITY

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Name:                                                              Period                                             GL
                                                 U N IT 5 : S IM IL A R I T Y
I can define, identify and illustrate the following terms:
Similar                          Cross products                         Scale Factor                          SAS ~
Similar Polygons                 Similarity Ratio                       Indirect measurement
Ratio                            Similarity Statement                   AA ~
Proportion                       Geometric Mean                         SSS~

                         Dates, assignments, and quizzes subject to change without advance notice.

                           Monday                   Tuesday                Block Day                 Friday
                   13                       14                       15/16                  17
                   Ratios and Proportions        Similar Figures        Similar Triangles        Geometric Mean
                   20                       21                       22/23
                          HOLIDAY                  Review            Test: Similarity
Monday, 2/13/12
Ratios and Proportions
        I can write and simplify ratios.
        I can solve problems using ratios.
        I can solve problems using proportions.
PRACTICE: Ratio and Proportions Worksheet
Tuesday, 2/14/12
Similar Figures
    I can determine if polygons are similar.
    I can write similarity ratios and statements for similar polygons.
    I can use the properties of similar polygons to solve problems.
PRACTICE: Similar Figures Worksheet
Block Day, 2/15-16/12
Similar Triangles
    I can determine if two triangles are similar using similarity postulates/theorems.
    I can use the properties of similar polygons to solve problems.
PRACTICE: Similar Triangles Worksheet
Friday, 2/17/12
Geometric Mean (8.1)
    I can apply similarity relationships in right triangles to solve problems.
    I can use geometric means.
PRACTICE: Geometric Mean Worksheet
Tuesday, 2/21/12
Review
PRACTICE: REVIEW WORKSHEET

Block Day, 2/22-23/12
   Test Unit #11: Similarity
Notes: Ratios

A ________ compares two numbers by division. The ratio of a and b is expressed as _________ or
_________ or ______.
Examples
In Mr. Alexander's Geometry class, there are 12 boys and 16 girls. Write the following ratios.
1. Boys to Girls                       2. Girls to Students                   3. Girls to Boys


4. In the United States House of Representatives there are 435 seats. Of those, 70 are occupied by women.
    Write the ratio of men to women in the US House of Representatives.


You can also use ratios to solve problems.

6. The ratio of the lengths of an isosceles triangle is 4:4:7, and its perimeter is 52.5 cm. What are the lengths
   of the sides of the triangle?




One common ratio is slope, which is the comparison of the ________ ___ ___ to the _________ ___ ___.
This can also be expressed as __________, the ________ ___ __________ or _____.

7. Write the ratio expressing the slope of the line.          8. Write the slope as a ratio for points
                                                                 A(7, 9) and B(2, -6).




Notes: Proportions

A proportion is an equation stating that two _________ are equal. You solve proportions by ___________
_____________________. When you cross multiply you create __________ cross products. For example in
                 a c
the proportion    = , ad = _____ . Once you have cross multiplied you need to __________ for the
                 b d
variable using algebra. (There are 4 ways to set up any proportion and still get the correct answer.)

      4   k                                  4 p                                      3   4
9.      =                              10.    =                               11.       =
     10 65                                   p 9                                    x +3 x+8
                 a 5
12. Given that    = , complete the following equations.
                 b 7
                         b                         a                         7
7a =                       =                         =                         =
                         a                         5                         b

To solve an application using proportions follow these steps:
   1. Read the problem carefully
          a. Are there any "tricks"? (percents, feet and inches mixed, multiple steps, etc)
   2. Draw a picture (if needed)
   3. Set up a proportion
   4. Solve the problem

13. The scale of a map of downtown Dallas is 1.5 cm: 300 m. If the distance between Union Station and the
   Dallas Public Library is 6 cm, what is the actual distance?




14. The $250,000 budget for a local shelter is allocated proportionally to the men's and women's
   departments according to the population in the shelter by gender. If there are 1946 women and 399 men
   in the shelter, what amount rounded to the nearest dollar is allocated to the men's department.




15. After an election in a small town, the newspaper reported that 42% of the registered voters actually
   voted. If 12,000 people voted, how many people are registered to vote in the town?




16. A student wanted to find the height of a statue of a pineapple in Nambour, Australia. She measured the
   pineapple's shadow at 8 ft 9in and her own shadow at 2 ft. The student's height is 5 ft 4 in. What is the
   height of the pineapple?




17. The Lincoln Memorial in Washington, D.C., is approximately 57 m long and 36 m wide. If you would
   want to make a scale drawing of the base of the building using a scale of 1 cm: 15 m, what would be the
   dimensions of the scale drawing?
                                   Ratio and Proportion Worksheet
                               s u                      n
1. Write the cross products for =
                               t w
                                                                                        a
                                                       m
Write the ratio expressing the slope of each line.                                      l
2. n                   3. a


4. Given that 2 points on line m are (-5, 0) and (1, -6)
   write a ratio that expresses the slope of line m.



5. During the 2003 NFL Season, the Dallas Cowboys won 10 of their 16 regular season games. What is the
   ratio of wins to losses?

6. The ratio of the side lengths of a quadrilateral is 2: 4: 5: 7, and its perimeter is 36 m. What is the length of
   the shortest side?


7. The ratio of the angle measures in a triangle is 5: 12: 19. What is the measure of the largest angle?


8. The ratio of the side lengths of an isosceles triangle is 4: 4: 7, and its perimeter is 52.5 cm. What is the
   length of the base of the triangle?


Solve the following proportions
  x 40                          y 27                         3 x 15                          x-6 x-9
9. =                         10. =                     11.      =                      12.      =
  2 16                          3  y                          5   x                           4   2


.
13. An 18-inch stick breaks into three pieces. The ratio of the lengths of the pieces is 1: 4: 5. Which of these
   is NOT a length of one of the pieces?
   A) 1.8 inches              B) 3.6 inches          C) 7.2 inches            D) 9 inches

                                               3 x
14. Which of the following is equivalent to     = ?
                                               5 y
        3 5                                                  x y
   A)    =                     B) 3x = 5y              C)     =                D) 3(5) = xy
        y x                                                  3 5

15. A recipe for salad dressing calls for oil and vinegar in a ratio of 5 parts oil to 2 parts vinegar. If you use
   1  cups of oil, how much vinegar will you need?
   A) 1                        B) 5                    C) 2                    D) 6 
          2                         8
16. Find the length of AB after the dilation.
                        A'
       A
                    6m
       4m                    10 m

              C          B
                              C'            B'
                                                           8 in
17. Which of the following could NOT be an enlargement or
    reduction (dilation) of the original painting?                 12 in




A      4 in                  B                   C 10 in                   D. 12 in
                             9in
                  6 in

                                    13 in                                             18 in
                                                           15 in

 18.


 19.




20.




 21.




 22.
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