1. Geometry Journal Chapter 7 & 8 By: Jaime Rich

2. A comparison of two numbers by division. An equation stating that two ratios are equal. You solve proportions by cross products or cross multiplication. You check if they are equal if the product of the cross multiplication are equal to each other. Proportions are related to ratios because proportions are made up of ratios.

3. RatiosProportions 5:10 5/10 5 to 10 5:10 = 1:2 5/10 = 1/2 5 to 10 = 1 to 2 Solving Proportions

4. Their corresponding angles are congruent and their corresponding side lengths are proportional. A similarity ratio is the ration of the lengths o f the corresponding sides of two similar polygons. Shows how much a figure is enlarged or reduced.

5. 16 8 3 6 90 55 35 80 50 6 4 12 18

6. Any method that uses formulas, similar figures, and / or proportions to measure and object. You can measure high, or big objects without physically measuring it with a ruler or Measuring tape. You can know distances from one place to another, and you can do many other things for planning for example to know where to build your house besides a tree pretending that tree may fall (you measure the height of the tree with indirect measurement and build the house away from it).

7. 2 ft 6 ft h 2/6 = 6/h 2h = 36 H = 36/2 H = 18 ft.

8. 4.5 ft h 3 ft 30 ft 3/4.5 = 30/h 3h = 135 h = 135/3 h = 45

9. h 100 ft 50 ft 2.5 ft 50/100 = 2.5/h 50h = 250 h = 250/50 h = 50 ft

10. Perimeter of small figure Perimeter of larger figure = x y Area of small figure Area of larger figure = x y -----> Then square root x/y and square that answer. If the similarity ratio of two similar figures is a/b, then the ration of their perimeters is a/b, and the ratio of their areas is a/b squared.

11. 5 7 10 15 21 30 22 / 66 = 2 / 6 = 1/3 The scale is 1 to 3 3 2.5 1 4 10 12 6.5/26 = 1/4 The scale is 1 to 4 1 1.5 4.5 3 2 3 6/9 = 1/1.5 The scale is 1 to 1.5

12. 5 7 3 2.5 1 4 10 12 1 1.5 4.5 3 2 3 21 30 17.5/157.5 = √(1/9) = (1/3) squared 1.5/24 = √(1/16) = (1/4)squared 1/2.25 = √(1/2.25) = (1/1.5)squared 10 15

13. Ratio of the length of the leg opposite the angle to the length of the hypotenuse. Ratio of the length of the leg adjacent to the angle to the length of the hypotenuse. Ratio of the length of the leg opposite the angle to the length of the leg adjacent to the angle.

14. To find the measurements of sides and angles of right triangles. You can use the Pythagorean theorem OR use sin, cos, or tan to solve it which is much faster and easier. You can also use the inverse trigonometric functions (sin-1, cos-1, and tan-1).

15. R 5 T 12 13 S SinR = 12/13 = 0.92 CosR = 5/13 = 0.38 TanR = 5/12 = 0.42 Cos( 76 ) 0.2419218956 Ex 1 Ex 2 Ex 3 Sin-1R = 67 Cos-1R = 68 Tan-1R = 23

16. Angle formed by a horizontal line and a line of sight to a point below the line.

17. Angle of Depression Angle of Elevation

18. < of elevation < of depression