Complete the Statement

Complete the statement.

1. If then =2. If then =

Solve for x.

3. 4. (hint … foil then factor!)

Determine if the pair of triangles are similar, not similar, or it cannot be determined. If

they are similar, complete the similarity statement  ABC ~ ____ and list the theorem or

postulate used to prove the triangles similar. If they are NOT similar, leave this BLANK!

5.6. 7.

 ABC ~ ____ ABC ~ ____  ABC ~ ____

8. Find the value of x if RQ:QP:PR is 3:4:5

Given: LMN ~ PQR. Find the values of the variables.

9. x = ______y = ______z = ______w = ______

10. What is the scale factor of LMN ~ PQR? _____

11. What is the perimeter of PQR? _____

(hint … you will have to find a and b!)

12. What is the scale factor of the perimeter of PQR to the perimeter of LMN? ______

13. What is the scale factor of the area of PQR to the area of LMN? ______

For each problem, write a proportion and solve to find the value(s) of the variable(s).

(Drawings may not be drawn to scale)

14. 15.

16. 17. (The triangles are similar!)

18.19. 20.

21.22. 23.

24. 25. 26.

27. If the exchange rate of Canadian dollars to American dollars is 1 to .78, how much
American dollars is needed to buy a camera
marked $55 in Canadian dollars? / 28. ABC ~ DEF
List the congruent angles and write a statement of proportionality,
29. The perimeter of a rectangle is 24 inches. The ratio of the length to the width is 2:1. Find the length and the width of the rectangle. / 30. One recipe for cookies calls for 8 tablespoons of sugar. One serving makes enough for 6 people. How much sugar is needed to serve 15 people?
31. A photograph that is 6 cm high and 8 cm wide is enlarged to a print that is 12 centimeters wide. What's the enlarged height? / 32. A tree casts a shadow 23 ft long. At the same time of day, a 6 ft person casts a shadow that is 10 ft long. How tall is the tree?
33. Are the s similar if ABC has sides 6, 6, 10 and XYZ has sides of 4, 5, and 4? Why or why not? / 34. If the scale is 2:19 and the real boat is 89 ft. long, what is the length of the model?
35. Find the geometric mean of 6 and 24. / 36. The measures of the angles of a triangle are in the extended ratio of 4:5:9. What are the measures of the angles? What type of triangle is this?

37. The area of a rectangle is 4320 square inches. The ratio of width to length is 5:6. Find the ength and the width.

Given , find the value of x.

38. 39.

Find the height of each figure in the picture. Each one is an enlargement of the preceding

one. The smallest figure’s height is already given.

45.When a 2-meter stick (standing vertical) casts a shadow 3 meters long, a 30 meter tree

also casts a shadow. How far is the stick from the tree?

Draw and label a sketch. Then write a proportion and solve.

46.Robert Wadlow was the tallest human being ever recorded. When a 6-ft. stick cast a

shadow of 24 inches, Robert would cast a shadow of 35.7 inches. How tall (in feet) was he?

Draw and label a sketch. Then write a proportion and solve. (Careful with units!)

47.By drawing lines on a map, a triangle can be formed by the cities of Phoenix, Tucson,

and Yuma. On the map, the distance between Phoenix and Tucson is 8 cm, the distance between Phoenix and Yuma is 12 cm, and the distance between Tucson and Yuma is 17 cm. The actual straight line distance from Phoenix to Yuma is 230 km. Find the distances between the other pairs

of cities. Draw and label a sketch. Then write a proportion and solve.

48. Are all equiangular triangles similar? Why or why not?