1. 7.1 Ratio and Proportions

2. Ratio and Proportion _______________________________________
________________________________________
Word form:
Colon form:
Fraction form:

3. A poster is 3 feet long and 20 inches wide
A poster is 3 feet long and 20 inches wide. Find the ratio of length to width.
Comparing feet:
Comparing inches:

4. Find the ratio of AE to BE.60 A 10 60 E 30 5x B
Find the ratio of AE to BE.
Find the ratio of the largest angle of Triangle A to smallest angle of triangle B.

5. 3. A telephone pole 7 meters tall snaps into. two parts
3. A telephone pole 7 meters tall snaps into two parts. The ratio of the two parts is 3:2. Find the length of each part.

6. A B 6 C D 10

7. The measures of the angles of a triangle are in the ratio of 3:4:5
The measures of the angles of a triangle are in the ratio of 3:4:5. Find the measures of each angle.

8. 7.2 Properties of Proportions

9. A proportion is a set of two equal ratios:
_____________________________________

10. The Means and Extremes Property:
_____________________________________
______________________________________

11. Properties of Proportions:

13. If CE=2, AB=6 and AD=3 then EB=______
2. If AB=10, DB=8 and CB=7.5 then EB=______

14. Find BD=______ DA=_____C E
BA=12, BE=10, EC=5
Find BD=______ DA=_____

15. 7.3 Similar Polygons

16. __________________________________________
Two polygons are similar if their vertices can be paired so that:
_________________________________________

17. List congruent Angles:B W A C V X Y Z E D
List congruent Angles:
List Proportions of sides:

18. If polygons are similar then the ratio of the lengths of two corresponding sides is called the Scale Factor 12 y D D` C C` 30 22 x z A` 50 B` A B 30
a) Scale Factor:
a) Find x, y, z:

19. The ratio of the perimeters of two similar figures is equal to the Scale Factor.12 z D D` C C` x
2.5 10 5 A` 3 B` A B y
a) Scale Factor:
a) Find x, y, z:

20. a) Scale Factor: b) Angle D`=____ c) Find CB, A`D`, DC: 21 D D` C C`60
100 6 5 A` 12 B` A B 4
c) Find CB, A`D`, DC:

21. 7.4 Proving Triangles are Similar

22. Postulate 15: ________________________
___________________________________ A X Y B C

23. When there are triangles within Trianlges:
_______________________________

24. Are the triangles similar? Find the scale factor._______
Solve for x=_______ 3 5 1 x

25. Find x=______ and y=______:
Scale Factor=____ x 8 3 y 3 4

26. A D O B C

27. 7.5 More Similar Triangles

28. Theorem 7.1: __________________________
______________________________________ 12 3 5 20

29. Theorem 7.2: ___________________________
_______________________________________ 12 28 3 7 5 20

30. How do we know what sides of the triangles to compare?
_______________________________________
________________________________________
__________________________________

31. What reason are the Triangles ~?6 10 3 5 3 5 6 6 6 10

32. Def of ~ ______________________________
______________________________________
Means and Extremes Property: __________
_____________________________________

33. A D
B C E

34. 10 x y 9 15 16
Solve for x and y: Scale Factor?____

35. 7.6 Proportional Lengths

36. Divide Proportionally means: ________________________________________
Triangle Proportionality Theorem:
____________________________________________________________________________________________________________ a c b d

37. Corollary: ____________________________
_____________________________________ a c b d

38. Triangle Angle Bisector:
_______________________________________ c a b d

39. Examples: 20 5x 10 5

40. x 10 12 24

41. x 4 2
x+2