1. Warm Up  Materials Needed: tape measure, pencil, and paper  With the assistance of your group members, record the following measurements:  Your wrist and your thumb measurement  Your arm span and your height  Your wrist and your neck  Describe any relationships you notice between the measurements.

2. Problem Solving with Proportions and Ratios Chapter 8.1-8.2 Objective: Students will be able to apply proportions to similar figures in real-world problems.

3. Ratio Review a to b a:b  ratios are usually expressed in simplest form  Simplify the ratios. a. b.

4. Example 1: The perimeter of rectangle ABCD is 60 centimeters. The ratio of AB:BC is 3:2. Find the length and width of the rectangle. D C length A width B

5. Proportions  proportion: an equation that equates two ratios Properties of Proportions  1.Cross Product Property: The product of the extremes equals the product of the means. If, then ad = bc.  2.Reciprocal Property: If two ratios are equal, then their reciprocals are also equal. If, then.

7. Central Park

9. Empire State Building

11. Times Square

13. The Statue of Liberty

14. For tourists visiting New York City, it can be hard to comprehend the actual size of the Statue of Liberty.

15. Your Task  To investigate the actual size of the Statue of Liberty’s nose  Given: The arm of the Statue of Liberty is 42 feet long.  Prove: The length of the Statue of Liberty’s nose.

16. Just to clarify:  The length of the Statue of Liberty’s nose means:  Measure from the bridge of your nose (where your nose start between your eyes)  End at the very tip of the nose  Arm length is from shoulder to the tip of your middle finger.

17. Hints…  What is the Statue of Liberty a statue of?  How long is your arm?  How long is your nose?

18. Actual Length: 4.5 feet

19. Example 2: International standard paper sizes are commonly used all over the world. The various sizes all have the same width-to- length ratios. Two sizes of paper are shown, called A4 and A3. Use the given measurements to find the value of x. A4A3 210mm x 420mm x

20. Geometric Mean geometric mean: two positive numbers a and b is the positive number x such that. If you solve the proportion for x, you find that x =. Find the geometric mean of 6 and 10.

21. Practice Time! 1.The perimeter of a rectangle is 40 feet. The ratio of the width to the length is 2:3. Find the length and the width. 2.The measures of the angles in a triangle are in the extended ratio of 2:4:8. Find the measures of the angles. 3.Find x, if AC:BC:AB is 2:1:2. 4 2x x+4 A B C

22.  Solve each proportion 1. 3. 2.

23. Cool Down  Write down three things you learned about ratios and proportions.