8.1 – Ratio and Proportion

1. 8.1 – Ratio and Proportion Solve Proportions Reduce Ratios Find unknown lengths given ratios

2. If a and b are two quantities that are measured in the same units, then the ratio of a to b is . It can also be written as a:b. Because a ratio is a quotient, the denominator cannot be zero. You also reduce ratios when possible, like 2:4 being 1:2 Given that there are 18 boys and 15 girls in class. Write the ratio of guys to girls Write the ratio of girls to guys Write the ratio of girls to students Does order matter? Why or why not?

3. To help with units: 1 ft = 12 in, 3 ft = 1 yard 5280 ft = 1 mi, 100 cm = 1 m 1000 g = 1 kg, 16 oz = 1 lb 1000 m = 1 km Generally, I’d convert to smaller units

4. Ratio between the length and width of a rectangle is 3:2. The perimeter is 30. Find the length of each side What do they want you to find? What information is given? What formula do you think you’ll need? How can you represent the information you need to find? Solve the problem What steps do you think are required to solve these types of problems?

5. Ratio between to supplementary angles is 10:8 Ratio of three sides of a triangle is 5:6:7. The perimeter is 54. Ratio of angles of a triangle is 1:2:3.

6. When you equate two ratios, it’s called a proportion. Extremes – First and last terms Means – Middle terms Cross-product property

7. A Setting up Proportions. B D C The ratio of AB to AD is 3:5. If AB = y + 2, and AD = 3y – 2, find y. The ratio of AD to CD is 1:3. If AD = x + 2, and CD = 6x, find AD.

9. A miniature goat is 12 inches tall, while a regular goat is 42 inches tall. If a regular goat body is 50 inches long, then how long is the body of a miniature goat? If a miniature goat’s leg is 2 inches tall, how tall is the regular goat’s leg?

10. 8.2 – Problem Solving in Geometry with Proportions Solve Proportions Geometric Mean Find unknown sides

11. If a, b, and x are positive, x is called the GEOMETRIC MEAN between a and b. x x a a = = x x b b Find the geometric mean between 4 and 20. Find the geometric mean between 8 and 24.

12. More Properties of proportions:

13. Decide if the statement is true or false

14. N O M L E NO OL NL NM ME NE 4 2 8 NO OL NL NM ME NE 6 9 12

15. D C X Y A B Z AX XD AD AZ ZB AB 4 3 6 AX XD AD AZ ZB AB 5 6 9

16. Write down one comment or question that you have on the material so far this chapter, you may be randomly called on.

17. 8.4 – Similar Triangles8.5 – Proving Triangles are Similar

18. AA Similarity Postulate – If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. B A C

19. A C B D E F

20. Are these triangles similar? Why? (Use complete sentences) 12 16 12 9

21. 22.5 12 12 30 16 16

22. Are these triangles similar? Why? (Use complete sentences) 500 400 500 900

23. 500 12 15 400 500 900 10 8

24. 12 15 16 20 10 8

25. FIND THE SCALE FACTOR! Solve for the unknown variables. D 8 10 15 8+y 12 U U U S S S S 5 y K K C C C z

27. 8.6 – Proportions and Similar Triangles

28. T Q P R S D C M B A L Triangle Proportionality Theorem – If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally. Converse of Triangle Proportionality Theorem - If the sides are proportional, then the lines are parallel.

29. Theorem – If three || lines intersect two transversals, then they divide the transversals proportionally. R X S Y T Z Triangle Angle-Bisector Thrm – If a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the other two sides. F G D E

30. x 14 y 12 18 x 4 3 8 x 8 12 20

31. 8 12 9 12 20 x y x 6 15 40 x 20