Name Honors Geometry Final Exam Review

Transcription

1 Name Honors Geometry Final Eam Review Chapter 5 Use the picture at the right to answer the following questions. 1. AC= 2. m BFD = 3. m CAE = A 29 C B 71⁰ 19 D 16 F 65⁰ E 4. Find the equation of the line in slope-intercept form that contains the altitude from A of the triangle with vertices of A(3,2), B(-1,6) and C(-5,-3). Put your answer in slope-intercept form if possible. 5. Find the equation of the line in slope-intercept form that contains the median from C of the triangle with vertices of A(3,7), B(0,-2) and C(8,5). Put your answer in slope-intercept form if possible. 6. Find the equation in slope-intercept form of the perpendicular bisector of AB given the triangle with vertices of A(-3,-5), B(4,-2) and C(5,5). Put your answer in slope-intercept form if possible. 7. If the conditional statement is true, then its must also be true. (converse, inverse or contrapositive)

2 8. Two sides of a triangle are 5 and 8. Describe all possible values for the length of the third side. 9. Write an indirect proof for the following. Given: A D Prove: ABC DEF 10. Write an indirect proof for the following. In XYZW if m X 80, then XYZW is not a rectangle. 11. Put the angles (1, 2 and 3) in order from largest to smallest of the triangle given below ⁰ 2 2

3 Chapter 6 Questions 12. The following figure is a parallelogram. Find the values of and y. (+y)⁰ 130⁰ 85⁰ (-y)⁰ 13. Find the value of y in the figure below. D is the midpoint of AB and AB=2y-16 C A 4y+1 D 6y+16 B 14. The following figure is a rectangle. Find the values of, y and z. y⁰ 5 z⁰ The following figure is a trapezoid. Find the value of The following figure is a rhombus. Find DO. A B 4 O 7 D C 3

4 Determine if the following quadrilaterals can be proven to be parallelograms. If your answer is yes, provide the reason An isosceles trapezoid ABCD has coordinates of A(0,0) B(a,b) and D (c,0). Name the coordinates of C in terms of a, b and/or c. Chapter 7 Questions 21. The ratio of the measures of two supplementary angles is 11:4. Find the measure of each angle. 22. The measure of the consecutive angles of a quadrilateral are in the ratio 5:7:11:13. Find the measure of each angle. 23. Are an equilateral triangle and an equiangular triangle always, sometimes, or never similar? 24. Find the values of, y, and z in the similar polygons shown below y 20 z 36 4

5 25. Find the values of and y y The diagram shows a film being projected on a screen (not drawn to scale). LF = 6cm and LS = 24m. The screen image is 2.2 m tall. How tall is the film image? L Lamp F Film Image S Screen Image Determine if the following triangles are similar. If so write the postulate or theorem that justifies that the following triangles are similar. If they cannot be proven similar, write none Find the value of. 30. Find the value of and y Find the geometric mean of 16 and y 2 5

6 32. Find the values of, y and z. y z 6 2 Chapter 8 Questions 33. A triangle has side lengths of 7, 3, and 34. Is the triangle acute, right or obtuse? 34. The sides of a triangle have lengths, +4, and 20. Specify those values of for which the triangle is acute, with longest side 20. Find the values of and y in each diagram ⁰ y 45⁰ 45⁰ 45⁰ y 45⁰ 37. A rhombus has diagonals of length 4 and 10. Find the angles of the rhombus to the nearest degree. 6

7 38. A guy wire is attached to the top of a 75 m tower and meets the ground at a 65⁰ angle. How long is the wire? 39. A certain jet is capable of a steady 20⁰ climb. How much altitude does the jet gain when it moves 1 km through the air? 40. Two buildings on opposite sides of a street are 40 m apart. From the top of the taller building, which is 185 m high, the angle of depression to the top of the shorter building is 13⁰. Find the height of the shorter building. Find the missing sides and angles of the triangles. If more than one triangle eists find both. If no triangle eists, state so. m A 40 m C 50 a m C a b 4 b 8 c 8 c 7 7

8 Chapter 9 Questions Given triangle ABC with vertices of A(-4,2), B(-1,5) and C(-2,1) perform the indicated transformations. State the coordinates of A,B and C 44. Rotation of 90 degrees clockwise about the origin. 45. Translation 4 units to the right. 46. Reflection over the line y = A dilation with a scale factor of 2 whose center of dilation is the origin. Chapter 10 Questions 48. The length of a rectangle is 12 cm more than its width. Find the area of the rectangle if its perimeter is 100 cm. 49. The diagonals of a rectangle are 18 cm long and intersect at a 60⁰ angle. Find the area of the rectangle. 50. Find the area of an equilateral triangle with height 9. 8

9 51. Find the area of a rhombus with perimeter 68 and one diagonal The legs of an isosceles trapezoid are 10 cm. The bases are 9 cm and 21 cm. Find the area of the trapezoid. 53. An isosceles trapezoid has bases 12 and 28. The area is 300. Find the height and the perimeter. 54. Find the area of a regular octagon with radius Find the area of an equilateral triangle with radius Which is the better buy a 10 inch pizza costing $5 or a 15 inch pizza costing $9? 57. A target consists of four concentric circles with radii 1, 2, 3, and 4. Find the area of the second ring of the target. 9

10 58. Find the area of the shaded region. 4 O 59. A rectangle with length 16 cm and width 12 cm is inscribed in a circle. Find the area of the region inside the circle but outside the rectangle. Chapter 11 Questions 60. Find the height of a rectangular prism with length 4, width 6, and volume 144³. 61. Find the lateral area of a right heagonal prism with height 15 and base edges 3.2, 4.1, 4.2, 5.4, 4.9, and Find the volume of a regular square pyramid with height 5 in and slant height 13 in. 63. A regular pentagonal pyramid has base edge 4 cm and lateral area 80 cm². Find its slant height. 64. The volume of a cylinder is 64π cm³. If the height is 8 cm, find the lateral area. 10

11 65. Find the volume of a sphere inscribed in a cylinder with height 8 cm. 66. A cone and a hemisphere have the same height and base. What is the ratio of the volume of the cone to the hemisphere? 67. The heights of two hemispheric domes used for storage have a ratio of 1:3. If 20 gallons of paint are needed to paint the floor and the entire inside area of the smaller dome, how much paint is needed to paint the larger dome? Chapter 12 Questions 68. The radii of two concentric circles are 15 cm and 7 cm. A diameter AB of the larger circle intersects the smaller circle at C and D. Find two possible values for AC. 69. Draw two congruent circles with radii 6 each passing through the center of the other. Find the length of their common chord. 70. Circles P and Q have radii 6 and 2 and are tangent to each other. Find the length of their common eternal tangent AB. A B 11

12 Use the picture below to answer questions 71 and 72. X Y 30⁰ Z W 50⁰ T 71. mwx = 72. mxyt = 73. A plane 5 cm from the center of a sphere intersects the sphere in a circle with diameter 24 cm. Find the diameter of the sphere. 74. Find the measure of the arc cut off by a chord 12 cm long in a circle of radii 10 cm. 75. Quadrilateral ABCD is inscribed in a circle. m A, m B 2, and m C 20. Find the value of and m D. 76. Find mrs. R S 77. Find muv. R 55⁰ 60⁰ T U V 20⁰ S T 80⁰ U 12

13 78. Find the value of. 79. Find the value of Find the equation of the circle with center (2,3) and passes through the point (2, 6). 81. The equations of two circles are between their centers. 2 2 y 25 and ( 2) ( y 2) 16. Find the distance