Geometry Spring Semester Review


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1 hapter 5 Geometry Spring Semester Review 1. In PM,. m P > m. m P > m M. m > m P. m M > m P 7 M 2. Find the shortest side of the figure QU. Q Q QU. U U 3. In EFG, m E = 5 + 2, m F = , and m G = hoose the list that shows the sides correctly ordered from longest to shortest.. EG, FE, GF. FE, EG, GF. EG, FG, FE. GF, EG, FE 4. What type of triangle has sides that measure 12, 13, and 18?. an obtuse triangle. a right triangle. an acute triangle. a triangle cannot be formed using those lengths 5. etermine which set of numbers can be the lengths of the sides of a triangle.. 4,, 1. 4, 7, , 2, , 4.8, 12. The lengths of two sides of a triangle are 8 and 15. The length of the third side is between:. 8 and and and and If M is the midpoint of JK, m 1 > m 2, JL = + 2, and LK = + 14, write an inequality to describe the possible values of?. > 3. < 3. > 12 J. < 12 M 1 2 K L 8. Which is a possible value of? (3) 1
2 9. If =, m 3 = 0, and m 4 = 45, which are possible measures of and?. =, = 4. = 5, = 4. = 7, = 7. = 5, = hapter 8. Find Find Find, y, k, and m. = k= y= m= 11. Find Find The altitude of an equilateral triangle is cm long. Find the length of each side of the equilateral triangle cm. 3 2 cm. 4 3 cm. cm 1. One side of a square is s. Find a diagonal. s. 2 s. s s k m 45 y 17. VW = 5, WX = 7, and XY = 13. Find VY. V What is the diameter of the largest circular tabletop that can be passed through a doorway 7 ft by 3 ft?. 3 ft. 7 ft. 7. ft. 8.1 ft E. 21 ft 19. The perimeter of an isosceles right triangle is Find the length of the hypotenuse E. 8 2 W X Y
3 20. Each side of an equilateral triangle is. Find an altitude In RST, m S = 90. What does sin T equal?. ST RT. RS ST. RS RT. RT RS 22. certain right triangle has an acute angle with a measure of degrees. If cos = 5 13, what does the tan equal? none of these Which equation could be used to find the value of?. cos 7 =. sin 23 =.9. cos 42 =. tan 48 = guy wire attached to the ground at point is 50 m long and makes an angle of 58 with the ground. Suppose it were fastened at point, making angle of 70 with the ground. Which of the following are needed to calculate the new length of the wire? sin 58, sin 70. cos 58, cos 70. sin 58, cos 70. sin 70, cos ladder m long just reaches the top of a building and its foot makes a 7 angle with the ground. Which of the following equations could be used to calculate the height, h, of the building? I. sin 7 = h II. cos 14 = h III. cos 7 = h. I only. II only. III only. I and II only E. I, II, and III 2. The angle of depression from the top of a 120 foot lighthouse looking down on a ship is 44. How far is the ship from the lighthouse? ft ft ft ft 27. cat sitting yards from the bottom of a tree is looking up at a bird s nest. The angle of elevation is 70. How high up in the tree is the nest? yd yd yd yd
4 28. treasure map gives the following directions: from the old stump take 30 paces east, 20 paces north, paces west, and 25 paces north. How far from the old stump is the treasure? hapter Use parallelogram for the net 4 questions. 29. m = 2, find m E 30. E = 3, E = 5 4, and =. Find E m = 2 + and m = What is the measure of? Use rhombus EFGH for the net 2 questions. 32. Find m FHE Find GH Use rectangle JKLM for the net 2 questions. 34. Find m JLK KP = 5 4, PL = , find G J M F 4 8 M P 30 H K L E Use square PQRS for the net 2 questions. 3. m SQR = 5 5. Find SQ P S 35 W Q R
5 Use isosceles trapezoid TRP for the following 2 questions. 38. m T 54 R 39. XY is the median and TR = 7 8, XY = 5 +, P = 4 4, find X P Y Use isosceles trapezoid for the following question. 40. Find m oth pairs of opposite sides of a quadrilateral are parallel. Which special kind of quadrilateral must it be?. parallelogram. rectangle. rhombus. trapezoid 42. The diagonals of a certain quadrilateral are equal. Which term could not be used to describe the quadrilateral?. isosceles trapezoid. rectangle. rhombus. square 43. diagonal of a parallelogram bisects one of its angles. Which special kind of parallelogram must it be?. rectangle. rhombus. square. parallelogram with a 0 angle 44. If EFGH is a parallelogram, which of the following must be true?. m E = m F. m F = m H. FG GH. m E + m G = Which information does not prove that quadrilateral is a parallelogram?. and bisect each other.. ; =. ; =. m = m ; m = m 4. For quadrilateral WXYZ it is known that WX = YZ. Which of the following additional pieces of information is not sufficient to prove that WXYZ is a parallelogram?. WX YZ b. XY = WZ. XY WZ. W is supplementary to Z. WY is the perpendicular bisector of XZ
6 47. In quadrilateral TUVW, TW UV. What additional information is needed to prove that TV bisects WU? I. TU WV II. TW = UV III. TU = WV. I only. II only. III only. I or II E. I or II or III 48. rhombus is also a square only if it is also a(n):. Parallelogram. Trapezoid. Rectangle. Equilateral Quadrilateral E. onve Polygon 49. is a quadrilateral with m = 2, m = 315, m = 4 90, and m = What can you conclude? I. m = 90 II. is a rectangle III. is a parallelogram. I only. I and III only. III only. I, II, and III E. None of These 50. RS UT, RV = VT, and RT bisects URS. Which of the following best describes RSTU? (The figure is not drawn to scale.). parallelogram. rhombus. rectangle. square E. none of these 51. etermine the quadrilateral that the following coordinates create (the most specific) y E(2,5), F(4,1), G(0,5), and H(,1). parallelogram. rectangle. rhombus. square E. none of the above 52. Find the area of the quadrilateral identified above. 53. Find FH. 54. Name the point at which the diagonals intersect. y 55. Find the area of triangle with the coordinates (2, 4), (4, ), and (5, 3)
7 hapter 5. Find the area. 57. Find the area Find the area. 59. Find the area Find the area of the shaded region π π π. 144π 2. Find area of shaded triangle Find the area Find the area Find the area of the following region created by three semicircles and an equilateral triangle. 12 cm 5. What is the area of an equilateral triangle with perimeter 24? What is the area of a triangle with sides 15, 15, and 24?
8 7. rhombus has diagonals and 8. What is the area? parallelogram and a triangle have equal areas. The base and height of the parallelogram are 12 and 9. If the base of the triangle is 3, find its height What is the area of trapezoid? Two base angles of an isosceles trapezoid have measure 45. The bases have lengths cm and 14 cm. Find the area of this figure. 71. The hypotenuse of a right triangle is 9 centimeters longer than one leg and 2 centimeters longer than the other. What is the perimeter of the triangle?. 17 cm. 40 cm. 8 cm. 2 cm 72. square is inscribed in a circle with radius 3. What is the area of the square? The area of a circle is 25π. What is its circumference?. 5π. π. 12.5π. 50π 74. triangle has an area of 28 square inches. The base of the triangle is inches less than twice the height. What is the length of the base of the triangle?. 5 inches. 4 inches. 7 inches. 8 inches 75. square is turned into a rectangle by decreasing one dimension by and decreasing the other dimension by 5. The area of the new rectangle is 135 less than the area of the square. Find the side of the original square One side of a rectangle is 14 and the perimeter is 44. What is the area?
9 77. square is circumscribed about a circle. Find the radius of the circle in terms of the length of a side of the square Mitch wants to use 40 feet of fencing to enclose a flower garden. Which of these shapes would use all the fencing and enclose the largest area?. rectangle with a length of 8 feet and a width of 12 feet.. n isosceles right triangle with a side length of about 12 feet.. circle with a radius of about 5. feet.. square with a side length of feet. 79. The dimensions of the small triangle are onethird those of the large triangle. point is picked at random within the large triangle. What is the probability that the point selected is within the small triangle? irections: The following four questions each consist of two quantities, one in olumn and one in olumn. ompare the two quantities and in the answer blank write:. if the quantity in olumn is greater. if the quantity in olumn is greater.. if the two quantities are equal. if the relationship cannot be determined from the information given. 80. olumn olumn The area of a regular octagon of side 12. The area of a regular pentagon of side The hypotenuse of an isosceles right The side of a square of area 8. triangle of area The area of a rhombus of side. The area of a square of side. 83. The area of region I. The area of region II. E I me = 135 II G F G = 2F 84. is a square inscribed in O and = 8. Find the area of the shaded region.. 1π π π π E. 1π O
10 85. In the diagram, what is the length of?. 2. π. 3π. 3π 8. In the diagram, what is the area of the shaded region?. 9π 3. 12π 3. 9π π 18 O 87. Find the length of a 45 arc in a circle of radius. hapter solid figure is formed by rotating the shaded region about the ais. What is the volume of the solid formed? 89. solid figure is formed by rotating the shaded region about the y ais. What is the surface area of the solid formed? 90. Given the surface area of the rectangular prism is 288, what is?
11 91. The drawing represents the view from directly above a solid figure that was built with cubes. Which drawing below shows a solid figure that would have this view from directly above? Find the total surface area of a cylinder with radius 4 and height.. 1π. 32π. 48π. 80π 93. The slant height of a regular square pyramid is 8 cm, and the length of each side of the base is cm. Find the lateral area.. 24 cm cm 2. 9 cm cm The surface area of a sphere is 324π square cm. Find the volume of the sphere π cm π cm π cm π cm What is the volume of a regular square pyramid with base edge 1 and height? What is the lateral area of the pyramid in the previous problem? sphere has area 1π. What is its volume?. 8 π π 3. 4 π π What is the volume of a rectangular solid with dimensions 12, 9, and? What is the total surface area of the solid in the previous problem?
12 0. cone has radius 5 and height 12. cylinder with radius has the same volume as the cone. What is the cylinder s height? How many square inches, of the cake shown, will need to be covered with icing? Find the volume of this regular heagonal prism cm cm cm cm 3 3. Find the total surface area of this regular heagonal prism. 4 5 cm 4. Find the volume of the space between the cylinder and the rectangular prism to the nearest cubic inch in in in in 3 5 in 12 in 1 in 5. The total volume of the figure at right is:. 45π cm 3. 0π cm 3. 30π cm 3. 90π cm 3. Find the total surface area. 13 in cm 5 cm 3 cm 7. The area of the top face of a rectangular prism is 54 square inches. If the volume is 12 cubic inches, which could be the dimensions of the rectangular prism.. 2 in 3 in 18 in. 2 in 9 in 9 in. 3 in in 9 in. in in 9 in
13 irections: The following three questions each consist of two quantities, one in olumn and one in olumn. ompare the two quantities and in the answer blank write:. if the quantity in olumn is greater. if the quantity in olumn is greater.. if the two quantities are equal. if the relationship cannot be determined from the information given. olumn olumn 8. Volume of a sphere with radius 4 cm Volume of a cone with radius cm and height 2 cm 9. Total area of a right triangular prism Total area of a regular square pyramid with all with all edges 7 m edges 7 m 1. Volume of a cylinder with radius 3 in Volume of a right rectangular prism with base and height 12 in. edges 3 in. and height 12 in cylinder with a height of 1.5 inches has a total surface area of 4 square inches. What is its approimate radius? in in in.. 2 in The volume of the larger prism is 128 cm 3. If the prisms are similar, what is the volume of the smaller prism?. 27 cm cm cm 3. 9 cm 3 4 cm 3 cm 113. The scale of two similar quadrilaterals is 1:2. The perimeter of the smaller quadrilateral is 80 centimeters. What is the perimeter of the larger quadrilateral?. 40 cm.. 80 cm.. 10 cm cm The cone is twice the height of the cylinder. Find the ratio of the volume of the cone to the volume of the cylinder.. 2:3. 3:2. 4:3. 2: Two similar pyramids have volumes 27 and 125. If the smaller has lateral area 18, what is the lateral area of the larger?
14 11. Find the total surface area of a cylinder with radius 4 and height.. 1π. 32π. 48π. 80π 117. Two similar cones have heights 4 and 1. What is the ratio of their volumes?. 1:4. 1:4. 1:1. 4:1 hapter, Find the measure of. (The figure is not drawn to scale.) What is the greatest possible distance between two points on a circle whose circumference is 2.8?. cm. 20 cm cm. 0 cm 120. Name an arc with a measure of YZ. WX. WZ. YW 121. If XW =, find the length of WZ.. π or π or.28. π or π or Given E = ; = 13, = 9, =. Find the perimeter of. Use circle E for these two problems Y X 0 E 20 Z W E J P G 123. The designated fishing area of a circular pond at a park is marked with two ropes attached to a buoy at the center of the pond. Each rope is 9 yards long, and together they form an angle of 170. What is the approimate area of the sector that is designated for fishing?. 120 yd yd yd yd 2 H
15 For the net 4 questions, refer to circle. XY is tangent and NY and YM are secants. Round to the nearest tenth. N 124. Find Y Find XY Find m NYM Find QM X 7 P 14 Y 1 0 Q M Use for these 4 problems 70 For the net 2 questions, find the value of. ssume that is the center of the circle Find the value of Find the value of If TPM = 54, what is the measure of T? If the measure of T = 2, = + 0 and T = 2 +, find the measure of T? M PT is tangent to M at T for both problems 132. Points,, and lie on a circle. is a diameter, and = 1. What is the measure of? In the previous problem, point is in such a position that is an inscribed quadrilateral. What is the sum of and? T P
16 134. If = 0 and = 30, what does X equal? X 135. If = 0 and = 30, what does 1 equal? If Y = j, Y = k, and Y = 7, what does Y equal? jk.. 7 j. 7k 7 k j 1 Y. 7 k j 137. Which of these equals XZ?. XYZ. OXM. XY 2. XOY X O M Y 138. If the radius is 13 and XZ = 24, what is the distance from O to any chord that is equal to XZ? Z 139. If OM = 8 and MY = 9, what does XZ equal?
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