2013-2014 Name Honors Geometr Final Eam Review Chapter 5 Questions 1. The following figure is a parallelogram. Find the values of and. (+)⁰ 130⁰ (-)⁰ 85⁰ 2. Find the value of in the figure below. D is the midpoint of AB and AB=2-1 C A 4+1 D +1 B 3. The following figure is a rectangle. Find the values of, and z. ⁰ 5 z⁰ 4. The following figure is a trapezoid. Find the value of. 2 Chapter Questions 5. If the conditional statement is true, then its must also be true. (converse, inverse or contrapositive). Two sides of a triangle are 5 and 8. Describe all possible values for the length of the third side. 7. Write the contrapositive and inverse of the following statement and determine whether each is true or false. Two skew lines do not intersect. 8. Write an indirect proof for the following. Given: A D Prove: ABC DEF
9. Write an indirect proof (proof b contradiction) for the following. In XYZW if m X 80, then XYZW is not a rectangle. 10. Put the angles (1, 2 and 3) in order from largest to smallest of the triangle given below. 3 1 140⁰ 2 Chapter 7 Questions 11. The ratio of the measures of two supplementar angles is 11:4. Find the measure of each angle.. The measure of the consecutive angles of a quadrilateral are in the ratio 5:7:11:13. Find the measure of each angle. 13. Are an equilateral triangle and an equiangular triangle alwas, sometimes, or never similar? 14. Find the values of,, and z in the similar polgons shown below. 21 15 18 20 15. Find the values of and. 4 z 3 15 2
1. The diagram shows a film being projected on a screen (not drawn to scale). LF = cm and LS = 24m. The screen image is 2.2 m tall. How tall is the film image? L F Lamp 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 the cannot be proven similar, write none. 10 17. 18. 9 10 7 9 15 8 19. Find the value of. 20. Find the value of and. 8 14 8 21 1 9 2 Chapter 8 Questions 21. Find the geometric mean of 1 and 24. 22. Find the values of, and z. z 2 3
23. A rectangle has length 2.4 and width 1.8. Find the length of the diagonal. 24. A right triangle has legs of and 8. Find the length of the median to the hpotenuse. 25. A triangle has side lengths of 7, 3, and 34. Is the triangle acute, right or obtuse? 2. The sides of a triangle have lengths, +4, and 20. Specif those values of for which the triangle is acute, with longest side 20. Find the values of and in each diagram. 27. 28. 30⁰ 45⁰ 45⁰ 45⁰ 45⁰ 29. The grade of a road is 7%. What angle does the road make with the horizontal? 30. A rhombus has diagonals of length 4 and 10. Find the angles of the rhombus to the nearest degree. 31. A gu wire is attached to the top of a 75 m tower and meets the ground at a 5⁰ angle. How long is the wire? 32. A certain jet is capable of a stead 20⁰ climb. How much altitude does the jet gain when it moves 1 km through the air? 33. 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. 4
Chapter 9 Questions 34. 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. 35. Draw two congruent circles with radii each passing through the center of the other. Find the length of their common chord. 3. Circles P and Q have radii and 2 and are tangent to each other. Find the length of their common eternal tangent AB. A B Use the picture below to answer questions 37 and 38. X Y 30⁰ Z W 50⁰ T 37. mwx = 38. mxyt = 39. 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. 40. Use trigonometr to find the measure of the arc cut off b a chord cm long in a circle of radii 10 cm. 41. Quadrilateral ABCD is inscribed in a circle. m A, m B 2, and m C 20. Find the value of and m D. 5
42. Find mrs. R S 43. Find muv. R 55⁰ 0⁰ T U V 20⁰ S T 80⁰ U 44. Find the value of. 45. Find the value of. 3 2 18 4. Find the equation of the circle with center (2,3) and passes through the point (2, ). 47. The equations of two circles are between their centers. 2 2 25 and ( 2) ( 2) 1. Find the distance 2 2 Chapter 11 Questions 48. The length of a rectangle is 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 0⁰ angle. Find the area of the rectangle. 50. Find the area of an equilateral triangle with height 9. 51. Find the area of a rhombus with perimeter 8 and one diagonal 30. 52. 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 and 28. The area is 300. Find the height and the perimeter. 54. Find the area of a regular octagon with radius. 55. Find the area of an equilateral triangle with radius 4 3. 5. Which is the better bu 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. 58. Find the area of the shaded region. 4 O 59. A rectangle with length 1 cm and width cm is inscribed in a circle. Find the area of the region inside the circle but outside the rectangle. Chapter Questions 0. Find the height of a rectangular prism with length 4, width, and volume 144³. 1. 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.2. 2. Find the volume of a regular square pramid with height 5 in and slant height 13 in. 7
3. A regular pentagonal pramid has base edge 4 cm and lateral area 80 cm². Find its slant height. 4. The volume of a clinder is 4π cm³. If the height is 8 cm, find the lateral area. 5. Find the volume of a sphere inscribed in a clinder with height 8 cm.. A cone and a hemisphere have the same height and base. What is the ratio of their volumes? 7. 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? 5. Construct a square.. Construct a regular heagon. 8