Sketch two similar triangles on paper. When drawing the similar triangles, make sure they are the same shape, but different in size. Make vertex A correspond to vertex D, vertex B correspond to vertex E, and vertex C correspond to vertex F. Label the proportional sides with the given information.

For the next six problems, refer to your drawing and write proportions to solve the problems.

1) EF = ______

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2) FD = ______

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3) Angle A is congruent to angle ______.

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4) Angle C is congruent to angle ______.

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5) Angle B is congruent to angle ______.

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6) What is the common ratio for the similar triangles that you drew?

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Refer to the similar triangles and given information shown below to solve the next three problems.

7) What is the (a) measure of “b” and (b) what proportion may be written to solve for “b”?

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8) What is the (a) measure of “c” and (b) what proportion may be written to solve for “c”?

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9) What is the scale factor of the larger triangle to the smaller triangle? Give the answer in decimal form.

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10) Refer back to the previous two problems to answer the following question. How could the scale factor be used to check the measure of “c”?

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11) For the similar triangles shown below, (a) what is the value of “x” (stated as a mixed number) and (b) explain how to solve the problem. Note that the triangles are rotated, so make sure to identify the correct corresponding sides.

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12) The figures shown below are similar. What is the PERIMETER of the smaller figure?

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13) For the following scenario, make a sketch of the similar triangles, label the proportional sides, and then solve. A thirteen-story building in an industrial park cast a 25-foot shadow. At the same time, a nearby 100-foot cell phone tower cast a 12-foot shadow. What is the height of the building? Round the answer to the nearest tenth.

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14) In the previous problem, a reasonable estimate would be to expect that the height of the building is (taller or shorter) than the height of the tower?

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15) For the following scenario, make a sketch of the similar triangles, label the proportional sides, and then solve. A fourteen-story hotel in an amusement park cast a 25- foot shadow. At the same time, a nearby 120-foot bungee jumping tower cast a 12-foot shadow. What is the height of the hotel?

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16) In the previous problem, a reasonable estimate would be to expect that the height of the building is (taller or shorter) than the height of the tower? Please explain.

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Review

17) Twenty five percent of Taylor’s dance class are age eight or under. There are 48 dancers in the class. How many dancers are OVER the age of eight?

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18) In the previous problem, (a) would it be a mistake if the calculated answer was less than 48? (b) What if the calculated answer was more than 48, would this be a mistake?

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19) Mrs. Thomas drives to work each day 75 miles one way. If she were in a hurry, could she legally drive to work in less than an hour with the legal speed limit set to 65 MPH. Use a formula to support your answer.

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20) Knowing that Mrs. Thomas (in the previous problem) lives close to an interstate highway, what is a good estimate of the amount of time she would need to hurry to work, but, still stay within the legal speed limit?

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In the next four problems sketch each solid, and then find the surface area of the solid based on the given dimensions. Label the answer appropriately.

21) Surface area of a pyramid: square base of 3 cm by 3 cm and slant height of 5 cm..

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22) Surface area of a rectangular pyramid: a base of 3 cm by 4 cm and slant height of 6 cm.

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23) Surface area of a square prism: base of 2 cm by 2 cm and height of 9 cm.

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24) Surface area of a cylinder: radius of 4.2 cm and a height of 10 cm. Round the answer to the nearest whole square centimeter.

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In the next two problems sketch each solid, and then find the volume of the solid based on the given dimensions. Label the answer appropriately.

25) Volume of a square prism: base of 3.2 mm by 3.2 mm and a height of 8 mm

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26) Volume of a cylinder: radius of 2.2 cm and height of 8.5 cm Round the answer to the nearest whole cubic centimeter.

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27) Which measure of volume in the previous two problems is more precise, cubic millimeters or cubic centimeters?

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28) The volume of a cylinder is 38.5 cubic centimeters and the height is 6 centimeters. What is the area of the base circle? Round the answer to the nearest hundredth. (Hint: Work backwards.)

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29) The volume of a triangular pyramid is 48 cubic centimeters and the height is 8 centimeters. What is the area of the base triangle?

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30) What is the area of a triangle with a height of six centimeters and a base of four centimeters?

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31) What is the area of a circle with a radius of six centimeters? Round the answer to the nearest tenth.

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32) What is the measure of an exterior angle of a regular nonagon (nine-sided polygon)?

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33) What is the measure of an interior angle of a regular nonagon?

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For the next two problems, refer to the chart below to convert from standard measure to metric measure.

34) 2 quarts (qt) = _______liters (l)

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35) 8 quarts = _______ liters (l)

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36) Estimate the square root to the nearest tenth.

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37) Estimate the square root to the nearest tenth

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38) Simplify.

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39) Simplify.

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40) Which inequality represents the solution for the given inequality?

a.) n < 4

b.) n > –18

c.) n < –4

d.) n > –4

41) For the inequality in the previous problem, list all integers between and including –5 and 5 that could be substituted in for “n” to make the inequality statement true.

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42) Solve for “z” using inverse operations.

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