A 20-foot flagpole is 80 feet away from the school building. A student stands 25 feet away from the building. What is the height of the student?

Transcription

1 Read each question carefully. 1) A 20-foot flagpole is 80 feet away from the school building. A student stands 25 feet away from the building. What is the height of the student? 5.5 feet 6.25 feet 7.25 feet 8.75 feet 1

2 2) A flagpole is 55 feet away from the school building. A 5-foot tall student stands 20 feet away from the building. What is the height of the flagpole? 11.5 feet feet 13 feet feet 2

3 3) Given the diagram below, what is the value of x? ) If a 5-meter flagpole casts a 10-meter shadow, how tall is a nearby house which is casting a 20-meter shadow? 5 meters 10 meters 15 meters 20 meters 3

4 5) A movie projector positioned 42 feet from a wall creates an image that is 8 feet wide on the wall. If a screen is placed 5 feet in front of the projector, what will be the width of the image on the screen? less than 1 foot between 1 and 2 feet between 2 and 3 feet greater than 3 feet 6) What is the value of y?

5 7) What is the value of y? ) What is the value of y?

6 9) What is the value of y? ) What is the value of y?

7 11) In the figure below, which value of x ensures that there are two similar triangles? There is no such value of x. 12) What is the value of y?

8 13) Which statement is true about the triangle below? x < 45 x > 45 x = 45 Not enough information to determine the value of x. 14) Which statement is true about the triangle below? x < 45 x > 45 x = 45 Not enough information to determine the value of x. 8

9 15) Which statement is true about the triangle below? x < 45 x > 45 x = 45 Not enough information to determine the value of x. 16) A ladder leaning against a building forms a 32-degree angle with the building. Which is closest to the height of the top of the ladder? 5 feet 9.4 feet 12.9 feet 15.1 feet 9

10 17) An airplane is 977 feet from the top of an air traffic control tower. Which is closest to the height of the air traffic control tower? 254 feet feet 723 feet feet 10

11 18) Which triangle was constructed congruent to the given triangle? 11

12 19) Which triangle was constructed congruent to the given triangle? 12

13 20) Which triangle was constructed congruent to the given triangle? 13

14 21) Which must be true? 22) 14

15 23) What are the sine, cosine, and tangent ratios of / P in the given triangle? 15

16 24) 16

17 25) 17

18 26) 18

19 27) 19

20 28) 20

21 29) 30) A right triangle's hypotenuse has length 14. If one leg has length 8, what is the length of the other leg? 21

22 31) 32) A square has a perimeter of 40 units. If the square is transformed so that its new perimeter is 20 units, what is true? The new area will be 25% smaller than the original. The new area will be 50% smaller than the original. The new area will be 75% smaller than the original. The new area will be the same as the original. 22

23 33) A right triangle has a perimeter of 24 units. If the triangle is transformed so that its new height is halved, what is true? The new area will be 25% smaller than the original. The new area will be 50% smaller than the original. The new area will be 75% smaller than the original. The new area will be the same as the original. 34) What is the value of y?

24 35) What reason can be used to prove that the triangles are congruent? AAS ASA SAS SSS 36) Two cars start at the same point on a straight road and travel 3 miles in opposite directions. Both cars then turn left on a perpendicular road and travel 4 miles. What is the distance between the two cars? 5 miles 10 miles 14 miles 25 miles 24

25 37) Which is true about P1 if it is the image of point P subject to a dilation with the center O and a scale factor k? For all values of k, P1 is on m. For k = 1, P1 is on m; for k > 1, P1 is in the shaded half-plane; for 0 < k < 1, P1 is in the non-shaded half-plane. For k = 1, P1 is on m; for k > 1, P1 is in the non-shaded halfplane; for 0 < k < 1, P1 is in the shaded half-plane. For all values of k, P1 is on a line parallel to m and removed from m by k units. 38) The diagram shows triangle MOP. Which statement would prove segment NQ is parallel to segment OP? distance from N to O is equal to the distance from Q to P distance from M to N is equal to the distance from M to Q slope of angle MOP is congruent to slope of angle QMN length of segment NO is equal to the length of segment MN 25

26 39) The diagram shows quadrilateral WXYZ. Which statement would prove WXYZ is a parallelogram? 40) Which of the following equations represents a line that is perpendicular to the line x + 4y = 12 and passes through the point (0, -9)? y = -4x - 9 y = 4x - 9 y = -0.25x - 9 y = -0.25x

27 41) What is true about the lines represented by this system of linear equations? y = -2x + 5 2y = x + 15 The lines are perpendicular. The lines are parallel. The lines coincide. The lines intersect, but are not perpendicular. 42) Which of the following equations represents a line that is parallel to the line 8x + 4y = -36 and passes through the point (0, 9)? y = -2x - 9 y = -2x + 9 y = -0.5x - 9 y = 0.5x

28 43) What is true about the lines represented by this system of linear equations? y = 6x - 9 y = 6x + 3 The lines are perpendicular. The lines are parallel. The lines intersect, but are not perpendicular. The lines coincide. 44) What is true about the lines represented by this system of linear equations? 4y = 2x y = -2x - 24 The lines are perpendicular. The lines are parallel. The lines coincide. The lines intersect, but are not perpendicular. 28

29 45) How are the graphs of the following functions different? The second graph will be perpendicular to the original graph. The second graph will intersect, but will not be perpendicular to the original graph. The second graph will be parallel to the original graph. The second graph will coincide with the original graph. 46) What is true about the lines represented by this system of linear equations? 3y = -2x + 6-6y = 4x - 12 The lines are perpendicular. The lines are parallel. The lines coincide. The lines intersect, but are not perpendicular. 29

30 47) What is true about the lines represented by this system of linear equations? y = 2x - 4 9y = 18x - 36 The lines are perpendicular. The lines are parallel. The lines coincide. The lines intersect, but are not perpendicular. 48) What is true about the lines represented by this system of linear equations? 4y = 2x y = 4x - 24 The lines are perpendicular. The lines are parallel. The lines coincide. The lines intersect, but are not perpendicular. 30

31 49) Which of the following equations represents a line that is perpendicular to the line x - y = 22 and passes through the point (0, -11)? y = -x - 11 y = x - 11 y = -x + 2 y = x ) What is true about the lines represented by this system of linear equations? y = -x - 16 y = x - 16 The lines are perpendicular. The lines are parallel. The lines coincide. The lines intersect, but are not perpendicular. 31