Final Exam Review. Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the length of.

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1 Final Exam Review Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Find the length of a. = 7 c. = 7 b. = 9 d. = 8 2. Find the best sketch, drawing, or construction of a segment congruent to. J K a. M c. G H L b. P d. R Q S 3. The map shows a linear section of Highway 35. Today, the Ybarras plan to drive the 360 miles from Springfield to Junction ity. They will stop for lunch in Roseburg, which is at the midpoint of the trip. If they have already traveled 55 miles this morning, how much farther must they travel before they stop for lunch? S 55 mi X R 360 mi a. 125 mi c. 180 mi b. 145 mi d. 305 mi J

2 4. Tell whether and are only adjacent, adjacent and form a linear pair, or not adjacent. F G a. only adjacent b. adjacent and form a linear pair c. not adjacent 5. n angle measures 2 degrees more than 3 times its complement. Find the measure of its complement. a. c. b. d. 6. Use the istance Formula and the Pythagorean Theorem to find the distance, to the nearest tenth, from T(4, 2) to U( 2, 3). a. 1.0 units c. 0.0 units b. 3.4 units d. 7.8 units 7. n animated film artist creates a simple scene by translating a kite against a still background. Write a rule for the translation of kite 1 to kite 2. y x 1 7 a. (x, y) (x 6, y + 6) c. (x, y) (x 2, y + 2) b. (x, y) (x + 6, y 6) d. (x, y) (x + 2, y 2) 8. Use the given two-column proof to write a paragraph proof. Given: 1 and 2 are supplementary... Prove: 3 is a right angle.

3 1 2 3 Two-column proof: Statements Reasons 1. 1 and 2 are supplementary. 1. Given and 2 are right angles. 2. ongruent supplementary angles form right angles. 3. m 3. efinition of a right angle efinition of congruent angles 5. m 5. Substitution 6. 3 is a right angle. 6. efinition of a right angle omplete the proof. Paragraph proof: is a given statement. Since [1], 1 and 2 are right angles. y the definition of a right angle, m. y the definition of congruent angles, [2]. Then, m by substitution. Therefore, 3 is a right angle by the definition of a right angle. a. [1] 1 and 2 are congruent angles [2] b. [1] by definition of a right angle [2] c. [1] congruent, supplementary angles form right angles [2] d. [1] m and m [2] 9. Find m in the diagram. (Hint: raw a line parallel to the given parallel lines.) 35º >> 1 130º >> a. m c. m

4 b. m d. m 10. Write and solve an inequality for x. 2x a. c. b. d. 11. for,,, and. Find a set of possible values for x and y. a. c. b. d. 12. is an isosceles triangle. is the longest side with length. = and =. Find. 4 x x +8 8 x + 3 a. = 110 c. = 43 b. = 24 d. = Find m, given,, and m. E F a. m c. m b. m d. m 14. Given:,,. T is the midpoint of.

5 R S Prove: T U omplete the proof. Proof: Statements Reasons Given 2. and are right angles. 2. [1] Right ngle ongruence Theorem Given [2] Given 7. T is the midpoint of. 7. Given efinition of midpoint [3] efinition of congruent triangles a. [1] efinition of right angles [2] Third ngles Theorem [3] Transitive Property of ongruence b. [1] efinition of perpendicular lines [2] Third ngles Theorem [3] Reflexive Property of ongruence c. [1] efinition of perpendicular lines [2] Vertical ngles Theorem [3] Symmetric Property of ongruence d. [1] efinition of perpendicular lines [2] Third ngles Theorem [3] Symmetric Property of ongruence 15. Show for. 6a - 2 a + 7 4a omplete the proof.

6 a. [1] [2] [3] 16 [4] 16 [5] SS.. by the Reflexive Property of ongruence. So by [5]. b. [1] [2] [3] 26 [4] 26 [5] SSS 16. pilot uses triangles to find the angle of elevation m? 40 c. [1] [2] [3] 16 [4] 16 [5] SS d. [1] [2] [3] 16 [4] 16 [5] SSS from the ground to her plane. How can she find 12 km 20 km O 20 km 12 km a. by SS and by PT, so m by substitution. b. by PT and by SS, so m by substitution. c. by S and by PT, so m by substitution. d. by PT and by S, so m by substitution. 17. Which of the following is not a positioning of a right triangle with leg lengths of 4 units and 5 units? a. y c. y x x

7 b. 8 y d. 8 y x x Given: Q is a right angle in the isosceles PQR. X is the midpoint of. Y is the midpoint of. Prove: QXY is isosceles. omplete the paragraph proof. Proof: raw a diagram and place the coordinates of PQR and QXY as shown. y P (0, 2 a) X Q(0, 0) Y R ([1], 0) y [2], the coordinates of X are x and the coordinates of Y are y [5], Since, by definition. So QXY is isosceles. a. [1] a [2] the istance Formula c. [1] a [2] the Midpoint Formula

8 [3], [4] [5] the Midpoint Formula [6], [7] [3], [4] [5] the istance Formula [6], 7] b. [1] 2a [2] the istance Formula [3] a, [4] a [5] the Midpoint Formula [6] a, [7] a d. [1] 2a [2] the Midpoint Formula [3] a, [4] a [5] the istance Formula [6] a, [7] a 19. Find the orthocenter of with vertices. a. c. b. d. 20. In, show that midsegment is parallel to and that. y (-4, 2) 2 K L x 2 (4, -2) (-4, -4) 4 a... The slope of. The slope of. The slopes are equal so. b. The length of. The length of.... The slope of. The slope of. The slopes are equal so. c. The length of. The length of.... The slope of. The slope of. The slopes are equal so. d. The length of. The length of.... The slope of. The slope of. The slopes are equal so.

9 height The length of. The length of Given with,, and, find the length of midsegment. = 6 X Y = 5 3 a. XY = 3 c. XY = 2.5 b. XY = 1.5 d. XY = Tell whether a triangle can have sides with lengths 1, 2, and 3. a. No b. Yes 23. Tell whether a triangle can have sides with lengths 4, 2, and 7. a. No b. Yes 24. The lengths of two sides of a triangle are 3 inches and 8 inches. Find the range of possible lengths for the third side, s. a. 5 < s < 11 c. 3 < s < 8 b. 3 < s < 11 d. 5 < s < The size of a TV screen is given by the length of its diagonal. The screen aspect ratio is the ratio of its width to its height. The screen aspect ratio of a standard TV screen is 4:3. What are the width and height of a 27" TV screen? 27" width a. width: 21.6 in., height: 16.2 in. c. width: 21.6 in., height: 5.4 in. b. width: 16.2 in., height: 21.6 in. d. width: 5.4 in., height: 21.6 in. 26. Find the measure of each interior angle of a regular 45-gon. a. 176 c. 172 b. 164 d Polygon EFGHIJKL is a regular dodecagon (12-sided polygon). Sides and are extended so that they meet at point O in the exterior of the polygon. Find m. a. m = 100 c. m = 120 b. m = 115 d. m = MNOP is a parallelogram. Find MP.

10 M N 5x 3x+12 P O a. MP = 25 c. MP = 20 b. MP = 30 d. MP = Show that GHIJ is a parallelogram for x = 5 and y = 8. H 5x-10 I 3y 5y-16 G 7x-20 omplete the explanation. J Given [1] GJ = 7(5) 20 = [2] Substitute and simplify. Given [3] [4] Substitute and simplify. Since HI = GJ and GH = JI, GHIJ is a parallelogram because [5]. a. [1] 15 [2] 15 [3] 24 [4] 24 [5] both sets of opposite sides are congruent. b. [1] 15 [2] 24 [3] 15 [4] 24 [5] one set of opposite sides is parallel and congruent. c. [1] 15 [2] 15 [3] 24 [4] 24 [5] both sets of opposite sides are parallel. d. [1] 24 [2] 24 [3] 15 [4] 15 [5] both sets of opposite angles are congruent. 30. Show that quadrilateral EFG is a parallelogram.

11 10 y E (3,. 10) (-5,7) 5 F(8, 4) G (0,1) 5 5 x omplete the explanation. and have the same slope, so [1]. Since E = FG, [2]. ecause [3], EFG is a parallelogram. a. [1] [2] [3] One pair of opposite sides is equal and perpendicular. b. [1] [2] [3] One pair of opposite sides is parallel and congruent. c. [1] [2] [3] One pair of opposite sides is parallel and in proportion. d. [1] [2] [3] One pair of opposite sides is not congruent but is perpendicular. 31. wooden frame has screws at,,, and so that the sides of it can be pressed to change the angles occurring at each vertex. and, even when the angles change. Why is the frame always a parallelogram? a. The angles always stay the same, so is a parallelogram. b. ll sides are congruent, so is a parallelogram. c. One pair of opposite sides is congruent and parallel, so is a parallelogram. d. One pair of opposite sides is congruent, so is a parallelogram.

12 32. Two vertices of a parallelogram are (2, 3) and (8, 11), and the intersection of the diagonals is the coordinates of the other two vertices. a. (12, 9), (6, 1) c. (11, 8), (5, 0) b., d.,. Find 33. Given: is a rectangle. W, X, Y, and Z are midpoints. Prove: WXYZ is a rhombus. X W Y omplete the proof. Z Proof: Statements Reasons 1. is a rectangle. 1. Given W, X, Y, and Z are midpoints. 2. are right angles 2. efinition of a rectangle Right ngle Theorem Theorem: oth pairs of opposite sides are congruent [1] ivision Property of Equality Reflexive Property of Equality Substitution efinition of ongruent Segments [2] PT

13 12. WXYZ is a rhombus 12. efinition of a rhombus a. [1] Midpoint Theorem [2] SS b. [1] efinition of Midpoint [2] SS c. [1] ivision Property of Equality [2] S d. [1] ivision Property of Equality [2] SS 34. The side of a wooden chest is a quadrilateral with. If m, what is the most accurate description of? a. oth pairs of opposite sides are parallel so is a parallelogram. Since one angle measures 90, it is a right angle and a parallelogram with one right angle is a rectangle. b. oth pairs of opposite sides are parallel so is a parallelogram. Since one angle measures 90, it is a right angle and a parallelogram with one right angle is a square. c. oth pairs of opposite sides are parallel so is a rhombus. Since one angle measures 90, it is a right angle and a rhombus with one right angle is a square. d. oth pairs of opposite sides are parallel so is a parallelogram. One angle measuring 90 does not provide enough information to change its description. 35. and. Find the value of x so that QRST is isosceles. R >> S Q >> T a. x = 2.8 c. x = 2 b. x = 0.8 d. x = Given:, Prove:

14 E omplete the proof. Proof: Statements Reasons 1., 1. Given 2., 2. Segment ddition Postulate 3. [1] 3. Substitution Property 4., 4. Simplify. 5., 5. ivision Property of Equality [2] [3] SS Similarity, steps 6 and 7 a. [1], [2] Transitive Property of Equality [3] Reflexive Property of ongruence b. [1], [2] Reflexive Property of Equality [3] Transitive Property of ongruence c. [1], [2] Transitive Property of Equality [3] Reflexive Property of ongruence d. [1], [2] Transitive Property of ongruence [3] Reflexive Property of Equality 37. The figure shows the position of a photo. Which of the following is the drawing of the photo after a dilation with scale factor?

15 5 5 a. 5 c. 5 ' ' ' ' ' ' 5 ' ' 5 b. 5 d. 5 ' ' ' ' ' ' 5 ' ' Write a similarity statement comparing the three triangles in the diagram.

16 G H F J a. c. b. d. 39. Find to the nearest hundredth. 2 4 a. = 0.45 c. = 2.24 b. = 0.50 d. = pilot flying at an altitude of 1.8 km sights the runway directly in front of her. The angle of depression to the beginning of the runway is 31. The angle of depression to the end of the runway is 23. What is the length of the runway? Round to the nearest tenth of a kilometer. a. 1.2 km c. 1.3 km b. 0.9 km d. 1.0 km 41. Find. Round to the nearest tenth a. = 13.8 c. = 33.8 b. = 10.4 d. = Write the vector in component form.

17 a. c. b. d. 43. Find the area of in terms of. Q 20 in. a. 400 c. 200 b. 100 d Find the area of the composite figure. 9 ft 12 ft 18 ft 9 ft a. 216 ft 2 c. 378 ft 2 b. 297 ft 2 d. 540 ft Find the shaded area. Round to the nearest tenth.

18 5 in. 6 in. a. c. b. d. 46. The radius of is multiplied by. escribe the effect of the change on the area. 12 in. a. The area is multiplied by 3. c. There is no effect on the area. b. The area is multiplied by. d. The area is multiplied by. 47. new music award for est Sound is a golden rectangle-shaped speaker. Each award represents sound that is considered twice as good as the previous award. Third place receives a 3 in. by 3 in. award. Second place receives a 6 in. by 6 in. award. First place receives a 12 in. by 12 in. award. Explain whether the overall size of the first place award is or is not misleading. 1st place 3rd place 2nd place a. Yes, the area of the 1st place award is four times as large as the 2nd place award, yet it represents sound only twice as good. b. Yes, the area of the 1st place award is three times as large as the 2nd place award, yet it represents sound only twice as good. c. No, the length of the 1st place award is twice as large as the length of the 2nd place, and it represents sound only twice as good. d. No, the width of the 1st place award is twice as large as the width of the 2nd place award, and it represents sound only twice as good. 48. When a certain SUV travels at 30 mph, it has a stopping distance of 50 feet. If a cardboard box falls off a truck between 30 to 70 feet in front of this SUV, what is the probability that the SUV will hit the box?

19 a. c. b. d. 49. raw all 6 orthographic views from the given object. ssume there are no hidden cubes. a. c. b. d. 50. raw a cylinder in one-point perspective. a. c.

20 b. d. 51. Find the drawing that represents the given object. ssume there are no hidden cubes. a. c. b. d. 52. Find the lateral area and surface area of a regular square pyramid with base edge length 6 m and slant height 8 m. a. lateral area: ; c. lateral area: ; surface area: surface area: b. lateral area: ; d. lateral area: ; surface area: surface area: 53. Find the lateral area and surface area of a right cone with radius 6 in. and height 8 in. Give your answers in terms of. a. lateral area: ; c. lateral area: ; surface area: surface area: b. lateral area: ; d. lateral area: ; surface area: surface area: 54. cone is created from a paper circle with a 90 sector cut from it. The paper along the remaining circumference of the circle is the base of the cone. Find the radius of the base of the cone. Round to the nearest hundredth.

21 15 cm a cm c cm b cm d cm 55. frustum of a pyramid is a part of the pyramid with two parallel bases. The slant height of the frustum of the pyramid is half the slant height of the original square pyramid. Find the surface area of the original pyramid, the lateral area of the top of the pyramid, and the area of the top base of the frustum. Then, find the surface area of the frustum of the pyramid. 8 cm 3 cm 6 cm a. Surface area of the original pyramid = 192 cm ; Lateral area of the top of the pyramid = 48 cm ; rea of the top base of the frustum = 9 cm ; Surface area of the frustum of the pyramid = 153 cm. b. Surface area of the original pyramid = 228 cm ; Lateral area of the top of the pyramid = 57 cm ; rea of the top base of the frustum = 9 cm ; Surface area of the frustum of the pyramid = 180 cm. c. Surface area of the original pyramid = 192 cm ; Lateral area of the top of the pyramid = 57 cm ; rea of the top base of the frustum = 9 cm ; Surface area of the frustum of the pyramid = 144 cm. d. Surface area of the original pyramid = 228 cm ; Lateral area of the top of the pyramid = 48 cm ; rea of the top base of the frustum = 9 cm ; Surface area of the frustum of the pyramid = 189 cm. 56. fish tank is in the shape of a rectangular prism. The height of the tank is 18 in. The width of the tank is 17 in. The length of the tank is 38 in. Find the amount of water the tank can hold to the nearest gallon. (Hint: 1 gallon ft 3.) a. 7 gallons c. 130 gallons

22 b. 50 gallons d. 7,231 gallons 57. The radius and height of the cylinder are multiplied by 4. escribe the effect on the volume. 3 cm 6 cm a. The volume is multiplied by 4. c. The volume is multiplied by 16. b. The volume is multiplied by 8. d. The volume is multiplied by Find the volume of the composite figure. Round to the nearest tenth. (Hint: Volume of a cone is.) 3 cm 6 cm 2 cm a cm 3 c cm 3 b cm 3 d cm Find the volume of the three-dimensional figure in terms of x. 3x 2 x + 1 x a. c. b. d.

23 60. Find the diameter of a sphere with volume in 3. a. in. c. in. b. in. d. in. 61. The radius of the sphere is multiplied by. escribe the effect on the volume. 7 in. a. The volume is divided by 2. c. The volume is divided by 4. b. The volume is divided by 3. d. The volume is divided by Name a line, a segment, and a triangle on the sphere. F G a. c. b. d. 63. lassify if =, >, and m.

24 F G a. obtuse scalene c. obtuse isosceles b. acute equilateral d. right isosceles 64. Two of the muscles that control eye movement are attached to the eyeball and intersect behind the eye as shown. If, what is? F a. = c. = b. = d. = 65. Tell whether the transformation appears to be a reflection. Explain. a. Yes; the image appears to be flipped across a line. b. No; the image does not appear to be flipped. 66. Which statement correctly describes a step in the process of drawing a reflection? a. Through each vertex draw a line perpendicular to the line of reflection. b. Measure the distance from each vertex to the line of reflection. Locate the image of each vertex on the same side of the line of reflection and the same distance from it. c. onnect the pre-images of the vertices. d. Measure the distance from each vertex to the line of reflection. Locate the pre-image of

25 each vertex on the opposite side of the line of reflection and the same distance from it. 67. In miniature golf, Saline wants to hit the golf ball (white circle) into the hole (black circle). She wants to accomplish this in one stroke, as easily as possible. Which statement best describes what she should do? l m a. Find the reflected image of the golf ball about line l. raw a line connecting the image to the hole. Mark the intersection of the line with line l. Saline should aim her stroke for this intersection. b. Find the reflected image of the golf ball about line m. raw a line connecting the image to the hole. Mark the intersection of the line with line l. Saline should aim her stroke for this intersection. c. Find the reflected image of the golf ball about line l. raw a line connecting the image to the golf ball. Mark the intersection of the line with line l. Saline should aim her stroke for this intersection. d. Find the reflected image of the golf ball about line l. raw a line connecting the image to the hole. Mark the intersection of the line with line m. Saline should aim her stroke for this intersection. 68. Reflect a figure with vertices across the x-axis. Find the coordinates of the new image. a. b. c. d. 69. Find that coordinates of the image of the point when it is reflected across the line. a. c. b. d. 70. Tell whether the transformation appears to be a translation. Explain. a. Yes; all of the points have moved the same distance in the same direction. b. No; not all of the points have moved the same distance. 71. Tell whether the transformation appears to be a translation. Explain.

26 a. Yes; all of the points have moved the same distance in the same direction. b. No; not all of the points have moved the same distance. 72. Which step does NOT describe a step in the process of drawing a rotation? a. onstruct a segment congruent to the given segment of rotation. b. raw a segment from each vertex to the point of rotation. c. onnect the images of the vertices. d. Measure the distance from each vertex to the point of rotation and mark off this distance on the corresponding ray to locate the image of each vertex. 73. nn wants to create a design to decorate her Geometry binder. She reflects part of the design across line p and then reflects the image across line n. escribe a single transformation that moves the part of the design from its starting position to its final position. p Start n Finish a. rotation of 180 about the origin c. translation along the line b. rotation of 90 about the origin d. reflection across the line 74. opy each figure and draw two lines of reflection that produce an equivalent transformation of translation to.

27 E F E' ' a. c. E E F M N F M E' ' E' ' b. F' d. F' E E F M N F M E' ' E' ' F' 75. opy the given figure and use it to create a tessellation. F' Step 1 Rotate the triangle about the midpoint of one leg of the triangle. Step 2 Translate the resulting pair of triangles to make a row of triangles. Step 3 Translate the row of triangles to make a tessellation.

28 Which of the following tessellations can you create from these steps? a. c. b. d. 76. etermine which of the following polygons cannot be used to form a tessellation. a. regular heptagon c. regular triangle b. regular hexagon d. rectangle 77. Which frieze pattern has glide reflection symmetry? a. c.

29 b. d. 78. Tell whether the transformation appears to be a dilation. Explain. a. Yes; the figures are similar, and the image is not turned or flipped. b. No; the figures are not similar. 79. Given the rectangle and the center of dilation P, which of the following is a dilation with a scale factor of 2? P a. c. P P b. d. P P 80. triangle with vertices,, and is given. Which of the following is the image of the triangle under a dilation with a scale factor of centered at the origin?

30 y x a. ' 12 y c. 12 y ' ' 4 ' x ' x ' 8 12 b. 12 y d. 12 y ' ' ' x x 4 ' ' 8 12 ' 8 12

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