Int Math 2B EOC FIG Assessment ID: ib C. DE = DF. A. ABE ACD B. A + C = 90 C. C + D = B + E D. A = 38 and C = 38

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1 If ΔDEF and ΔJKL are two triangles such that D J, which of the following would be sufficient to prove the triangles are similar? A. DE = EF JK KL B. DE = EF JK JL C. DE = DF JK KL D.

1 1 If ΔDEF and ΔJKL are two triangles such that D J, which of the following would be sufficient to prove the triangles are similar? A. DE = EF JK KL B. DE = EF JK JL C. DE = DF JK KL D. DE = DF JK JL 2 A diagram is shown below. Which statements show that ΔABE is similar to ΔACD? Select all that apply. A. ABE ACD B. A + C = 90 C. C + D = B + E D. A = 38 and C = 38 E. ADC = 102 and AEB = Use the figure below to answer the following question. If AC DE, which of the following justifies ΔABC ~ ΔDBE? A. Definition of Similar Triangles B. SAS Similarity Theorem C. SSS Similarity Theorem D. AA Similarity Postulate Generated On April 17, 2017, 2:49 PM PDT Page 1

2 4 What is the volume of the right cylinder pictured below? A. 69 π mm 3 B. 80 π mm 3 C. 150 π mm 3 D. 600 π mm 3 5 Which Diagram represents the figure with the greatest volume? A. B. C. D. 6 Mark did a survey to determine what the favorite food in his school was. He asked 50 students in his school what their favorite food was. The results are shown in the table below. Boys Girls Hamburgers 6 10 Pizza 12 8 Tacos 1 2 Hot Dogs 6 5 If Mark to randomly selects a boy, what is the probability that the boy's favorite food is tacos? A. 96% B. 8% C. 4% D. 2% Generated On April 17, 2017, 2:49 PM PDT Page 2

3 7 Mr. Ricketts is randomly distributing 25 hot chocolates and 20 iced coffees to his fellow board members. What is the probability that the first cup he hands out will be hot chocolate and the second cup will be an iced coffee? A. 5 B. 45 C. 5 D In a paper bag, 6 of the 18 marbles are blue. In a cloth bag, 1 of the 18 marbles is blue. If Stanley chooses one marble from each bag at random, what is the probability he will choose a blue marble from the paper bag and a blue marble from the cloth bag? A. 1 B. 7 C. 6 D Jessica and Kyle each bought one of the 250 raffle tickets sold at the county fair. If two tickets will be drawn and awarded prizes, what is the probability that both Jessica and Kyle hold winning tickets? A. 1 B. 1 C. 1 D ,625 31,125 62, A glass jar contains 1 red, 3 green, 2 blue, and 4 yellow marbles. If a single marble is chosen at random from the jar, what is the probability that it is yellow or green? A. 1 5 B. 2 7 C D Of 8 dogs in a kennel, 5 are male and 3 are female. If a trainer randomly chooses two dogs for a walk, what is the probability he will choose two females? A. 3 B. 3 C. 9 D Generated On April 17, 2017, 2:49 PM PDT Page 3

e = 50 16 Justin was asked to write six different equations based on the triangle below.

4 15 A student was asked to solve for each of the variables in the diagram below, rounding to the nearest tenth if necessary. Which three of the variables did the student solve correctly? A. a = 14.6 B. b = 6.7 C. c = 12.4 D. d = 20 E. e = Justin was asked to write six different equations based on the triangle below. Four of the six equations that Justin wrote are correct. Which four of the equations are correct? A. B. C. D. E. F. Generated On April 17, 2017, 2:49 PM PDT Page 4

5 17 A 32" flat screen television measures 32 inches across its diagonal. The diagonal makes a 35 angle with the bottom of the television. Select all equations that can be used to solve for the height, h, of the television screen. A. B. C. D. cos35 = h 32 sin35 = h 32 tan35 = h 32 cos55 = h 32 E. F. sin55 = h 32 tan55 = h Marcel walks due north 50 meters from a tree. Katya walks 20 meters in a straight line away from the same tree but at an angle of 42 from due north, as shown in the diagram below. How far apart are Marcel and Katya to the nearest meter? meters Generated On April 17, 2017, 2:49 PM PDT Page 5

6 19 Is there a method that could prove that these two triangles are similar? A. Yes, a sequence of dilations and rigid motions carries one triangle onto the other. B. Yes, showing that all pairs of corresponding sides are congruent. C. No, the triangles are not similar because we do not know the measurement of third angle. D. No, the triangles are not similar due to differences in size and side lengths. 20 Is there a method that could prove that these two triangles are similar? A. Yes, a sequence of dilations and rigid motions carries one triangle onto the other. B. Yes, showing that all of the corresponding sides are similar. C. Yes, showing that corresponding angles are congruent and all corresponding sides are proportional. D. No, the triangles are not similar due to different angle measurements. Generated On April 17, 2017, 2:49 PM PDT Page 6

21 A fountain is located between two trees. Each tree has a height of 60 feet. The angles of elevation from the base of the fountain to the top of each tree are 64 and 48 as shown below.

7 21 A fountain is located between two trees. Each tree has a height of 60 feet. The angles of elevation from the base of the fountain to the top of each tree are 64 and 48 as shown below. What is the horizontal distance between the two trees (rounded to the nearest foot)? A. 40 ft B. 83 ft C. 147 ft D. 190 ft 22 Right triangle XYZ is shown below. Enter the ratio equivalent to tan(x). tan(x) = Generated On April 17, 2017, 2:49 PM PDT Page 7

8 23 Consider right triangle ABC shown below. Which trigonometric ratios are equivalent to 5 13? Select all that apply. A. cos A B. sin A C. tan A D. cos C E. sin C F. tan C 24 Right triangle PQR is shown. Which trigonometric ratios are equivalent to 3 5? Select two that apply. A. cos P B. sin P C. cos R D. sin R E. tan R Generated On April 17, 2017, 2:49 PM PDT Page 8

9 25 Right triangles ABC and PQR are shown below, where A P. What is the area, in square inches, of triangle PQR? square inches 26 A roof has an overall height of 8 feet and a slant length of 17 feet. Which equations can be used to solve for the measure of A? Select all that apply. A. tan A = 8 15 B. sin A = 8 17 C. tan A = 15 8 D. cos A = E. cos A = 17 8 F. sin A = Generated On April 17, 2017, 2:49 PM PDT Page 9

10 27 Triangle FLR is similar to triangle MBT. Select all angles whose sine equals A. B B. F C. L D. M E. R F. T 28 Consider this right triangle. Select the ratio equivalent to tan(o). A. 5 B. 5 C. 12 D Generated On April 17, 2017, 2:49 PM PDT Page 10

11 29 On the diagram below, a boat, represented by point A, is 450 feet away from a buoy, represented by point B. Another buoy is located at point C. The three points form a right triangle with the measure of A equal to Enter the distance between the two buoys, rounded to the nearest foot. feet 30 Henry is painting a house. He placed a 24 foot ladder 15 feet away from the base of the house so that it leaned up against the house. Enter the measure of the angle that is formed between the ladder and the ground, rounded to the nearest tenth. 31 Consider this right triangle. Enter the value of side length x. Generated On April 17, 2017, 2:49 PM PDT Page 11

12 32 Triangle LMN is similar to triangle PQR. Select all angles whose sine equals A. L B. M C. N D. P E. Q F. R 33 A 254 foot tall radio tower is located partway between a building and a tree. The angle of elevation from the base of the building to the top of the tower is 36, and the angle of elevation from the base of the tree to the top of the tower is 62. What is the distance from the base of the building to the base of the tree (rounded to the nearest foot)? A. 485 feet B. 508 feet C. 662 feet D. 720 feet Generated On April 17, 2017, 2:49 PM PDT Page 12

13 34 Claire is constructing a triangular garden, shown below. If Claire would like to completely surround the garden with fencing, how much fencing will she need? A. 13 ft B. 17 ft C. 30 ft D. 34 ft 35 If a flagpole casts a 13 ft shadow on the ground when the sun is at a 68 angle of elevation, which of the following expressions can be used to determine the height (h) of the flagpole? (Assume the flagpole is at a right angle to the ground.) A. B. C. D. cos 68 = h 13 cot 68 = h 13 sin 68 = h 13 tan 68 = h While standing at the top of a lighthouse, Joel notices a boat approaching the shore. If the boat is 250 ft from the base of the lighthouse and Joel needs to look down at 41 angle of depression in order to see the boat, what is the approximate height of the lighthouse? (Assume the lighthouse is at a right angle to the ground.) sin cos tan A. 165 ft B. 188 ft C. 218 ft D. 287 ft 37 Haley planted a new tree in her yard. To help the tree to grow upright, she attached support wires to the tree. If the support wires are each attached 4 ft up the tree and form a 56 angle with the ground, what is the length of each support wire? sin cos tan A ft B ft C ft D ft Generated On April 17, 2017, 2:49 PM PDT Page 13

Given AE ED = BE, which of the following justifies ΔAEB ~ ΔDEC? EC A. Definition of Similar Triangles B.

14 38 Triangle PQR is similar to triangle XYZ. What is the perimeter of triangle XYZ? A. 3 in. B. 4 in. C. 12 in. D. 16 in. 39 What is the perimeter of ΔRST? A. B. C. D. 40 Use the figure below to answer the following question. Given AE ED = BE, which of the following justifies ΔAEB ~ ΔDEC? EC A. Definition of Similar Triangles B. SAS Similarity Theorem C. AA Similarity Postulate D. Triangle Proportionality Theorem Generated On April 17, 2017, 2:49 PM PDT Page 14

15 41 Find the value of x. A. 16sin(35 ) B. 16cos(35 ) C. sin(35 ) 16 D. 16 sin(35 ) 42 In the figure shown below, m C = 40 and AB = 8. Which equation could be used to find x? A. x = 8cos 40 B. x = 8sin 40 C. x = 8tan 50 D. x = 8tan In the right triangle below, if tan x = 8, then what are the ratios of sin x and cos x? 15 A. sin x = 17 8 and cos x B. sin x = 17 8 and cos x C. sin x = 8 17 and cos x D. sin x = 8 17 and cos x = = = = Generated On April 17, 2017, 2:49 PM PDT Page 15

44 Use the table below to determine the approximate height of the flag pole. A. 14.3 ft B. 17.5 ft C. 20.5 ft D. 35.7 ft 45 In the diagram below, AB and DE are parallel.

The student draws the parallelogram below, where the sides of the parallelogram have been extended. The student outlines a proof, as follows: "First, I'll show that 5 2. Then, I'll show that 5 4.

16 44 Use the table below to determine the approximate height of the flag pole. A ft B ft C ft D ft 45 In the diagram below, AB and DE are parallel. Which of the following statements must be true? A. C is a right angle B. D and E are congruent C. Triangles ABC and DEC are similar. D. None of the above 46 A student wants to prove that opposite angles of a parallelogram are congruent. The student draws the parallelogram below, where the sides of the parallelogram have been extended. The student outlines a proof, as follows: "First, I'll show that 5 2. Then, I'll show that 5 4. It must follow that 2 4. Next, I'll show that 1 6. Then, I'll show that 3 6. It must follow that 1 3. Since 2 4 and 1 3, it follows that opposite angles of a parallelogram are congruent." Which of the following congruence statements are based on the reasoning that alternate interior angles are congruent when two parallel lines are cut by a transversal? Select two that apply. A. 1 3 B. 1 6 C. 5 2 D. 5 4 Generated On April 17, 2017, 2:49 PM PDT Page 16

17 47 In the drawing below, lines a and b are parallel lines cut by the transversal c. Jeremiah wishes to find angles that are congruent to 7 in order to prove that 7 3 Which angles are congruent to 7? Why are they congruent to 7? Select two that apply. A. 8 because linear pairs are congruent B. 6 because vertical angles are congruent C. 4 because alternate interior angles are congruent D. 3 because corresponding angles are congruent 48 Examine parallelogram RSTU below. Determine which of the following values are correct. Select three that apply. A. x = 15 B. y = 23 C. m R = 27 D. m S = 135 E. m T = 45 F. m U = 99 Generated On April 17, 2017, 2:49 PM PDT Page 17

18 49 Examine the figure below. Determine which of the following angle measures are correct. Select two that apply. A. m ABC = 68 B. m BAC = 72 C. m BCD = 108 D. m ACB = Based on the following figure, determine which values below are correct. Select two that apply. A. x = 4 B. x = 6 C. x = 9 D. m ACB = 51 E. m ACB = 63 F. m ACB = In which of the following triangles does m A=62? Select three that apply. A. B. C. D. Generated On April 17, 2017, 2:49 PM PDT Page 18

19 52 Examine the properties listed below. Determine which of the following properties are true for all parallelograms. Select three that apply. A. four right angles B. diagonals bisect each other E. diagonals intersect at right angles C. opposite sides are congruent D. opposite angles are congruent 53 Examine parallelogram ABCD below. Determine which of the following values are correct. Select three that apply. A. x = 16 B. x = 19 C. m A = 75 D. m B = 87 E. m C = 93 F. m D = In the figure below, line a line b. If m 2 = 78, which of the following angles also measure 78? Select three that apply. A. 3 B. 4 C. 5 D. 6 E. 7 F. 8 Generated On April 17, 2017, 2:49 PM PDT Page 19

20 55 Examine parallelogram ABCD below. In order to determine the length of each side of the parallelogram, which of the following equations would need to be used? Select two that apply. A. 5x x 6 = 180 B. 9y 2 + 7y + 4 = 180 C. 5x + 12 = 8x 6 D. 9y 2 = 7y DE AC in the picture below. Which of the following statements must be true? A. A B B. A C C. AC = AD DE DB D. AC = BC DE BE 57 Transversal c intersects the parallel lines, a and b, in the picture below. What is the value of x? A. 78 B. 84 C. 96 D. 102 Generated On April 17, 2017, 2:49 PM PDT Page 20

21 58 In each diagram below, line a is parallel to line b. In which diagram does the Corresponding Angle Postulate justify angle 1 being congruent to angle 2? A. B. C. D. 59 In each diagram below, line r is parallel to line s. In which diagram MUST angle 1 be congruent to angle 2? A. B. C. D. Generated On April 17, 2017, 2:49 PM PDT Page 21

22 Directions: Read the passage below and answer the question(s) that follow. GEO 4.0 Angles 60 Given P Q and T is a transversal, which of the following justifies 3 6? A. Corresponding Angles Postulate B. Alternate Interior Angles Theorem C. Consecutive Interior Angles Theorem D. Alternate Exterior Angles Theorem Generated On April 17, 2017, 2:49 PM PDT Page 22

61 Find the value of x when lines w and v are parallel: A. 15.5 B. 17 C. 23.25 D. 29.5 62 A grain silo is shaped like a cylinder with a height of 24 feet and a diameter of 10 feet.

23 61 Find the value of x when lines w and v are parallel: A B. 17 C D A grain silo is shaped like a cylinder with a height of 24 feet and a diameter of 10 feet. A farmer wishes to determine how many cubic feet of grain could fit in the silo. What is the maximum amount of cubic feet of grain that the silo could hold? A cubic feet B cubic feet C cubic feet D. 600 cubic feet 63 A spherical shaped ball that has a radius of 4 inches is currently deflated. How much air would it take to completely inflate the ball? A. 512 in 3 B. 64 in 3 C π D. 3 in3 256 π 3 in3 64 Find the volume of a sphere with a diameter of 22m. Round to the nearest tenth. A. 44,579.6 m 3 B m 3 C m 3 D m 3 Generated On April 17, 2017, 2:49 PM PDT Page 23

65 Find the volume of the cylinder. Round the answer to the nearest hundredth. A. 216.97 ft 3 B.

64 ft 3 66 Find the volume of the pyramid and round to the nearest tenth. A. 33.3 cm 3 B. 37.

24 65 Find the volume of the cylinder. Round the answer to the nearest hundredth. A ft 3 B ft 3 C ft 3 D ft 3 66 Find the volume of the pyramid and round to the nearest tenth. A cm 3 B cm 3 C cm 3 D. 100 cm 3 67 Calculate the volume of the cylinder: A. 9πcm 2 B. 36πcm 2 C. 360πcm 3 D. 90πcm 3 Generated On April 17, 2017, 2:49 PM PDT Page 24

25 68 Calculate the volume of a square based pyramid with an altitude height of 6 ft and base edges of 8 ft. A. 64 ft 3 B. 128 ft 3 C. 192 ft 3 D. 384 ft 3 69 This figure shows a hemisphere attached to a cylinder. The cylinder has a diameter of 12 cm. The entire composite figure has a height of 23 cm. What is the volume of this composite figure? A. 756π cm 3 B. 828π cm 3 C. 900π cm 3 D. 972π cm 3 Generated On April 17, 2017, 2:49 PM PDT Page 25

26 70 If arc HJ =66, what is m HIJ? A B. 22 C. 33 D. 66 Stop: You have finished the assessment. Generated On April 17, 2017, 2:49 PM PDT Page 26

Radicals and Pythagorean Theorem Date: Per:

Math 2 Unit 7 Worksheet 1 Name: Radicals and Pythagorean Theorem Date: Per: [1-12] Simplify each radical expression. 1. 75 2. 24. 7 2 4. 10 12 5. 2 6 6. 2 15 20 7. 11 2 8. 9 2 9. 2 2 10. 5 2 11. 7 5 2