1. Bellwork Simplify Simplify Solve Solve The area of a rectangle is 750 square meters. The ratio of the width to the length is 5:6. Find the width and length. The area of a rectangle is 750 square meters. The ratio of the width to the length is 5:6. Find the width and length. Clickers

2. Bellwork Solution Simplify Simplify

3. Bellwork Solution Solve Solve

4. Bellwork Solution Solve Solve

5. Bellwork Solution Solve Solve

6. Bellwork Solution The area of a rectangle is 750 square meters. The ratio of the width to the length is 5:6. Find the width and length. The area of a rectangle is 750 square meters. The ratio of the width to the length is 5:6. Find the width and length.

7. Use Proportions to Solve Geometry problems Section 6.2

8. The Concept Yesterday we reviewed ratios and proportions and also talked about the relationship between two objects Yesterday we reviewed ratios and proportions and also talked about the relationship between two objects Now we’re going to suffuse the two concepts into a practical application of similar polygons Now we’re going to suffuse the two concepts into a practical application of similar polygons

9. Reciprocity Once concept that should be addressed before we continue is the concept of reciprocity This is illustrated by the bellwork and can be further elucidated via this figure These proportions are all similar statements. Why? Reciprocity is the ability to rewrite proportions in different manners and achieve the same answer

10. Common Ratios In the bellwork we talked about a ratio that exists between a length and a width. Many times we also see a common ratio that exists between two objects Let’s write the ratios that we see 3 4 5 A B C

11. Ratio Example These triangles show a common ratio Let’s now write the proportions that develop 3 4 5 A B C Can we now use these relationships to solve for the unknown sides? x y 30 D E F

12. Example Assuming a similar ratio exists, find the measure of FE A B C D E F G H 2 3 6 5 x+1 12 2y+2

13. Example Assuming a similar ratio exists, solve for y A B C D E F G H 2 3 6 5 x+1 12 2y+2

14. Practical Example The scale of a map is 1 in:1440 ft. Find the actual length of a street if the distance on the map is 3 inches.

15. Homework 6.2 6.2 1-6, 8-18, 22-33, 38, 39 1-6, 8-18, 22-33, 38, 39

16. Practical Example A road gradient is measured in percentages, where a 100% grade is a 45 o angle. Based on this information, what angle with the horizontal does a 40% grade make?

17. Most Important Points Using ratios in geometric relationships Using ratios in geometric relationships