3. Write a conditional statement ( If.., then ) from the sentence: A whole number is an integer. If, then.

Transcription

1 Geometry: Spring Semester Final Exam Review Worksheet Name Hour Score /30 1. Refer to the diagram at the right. a. Name 2 lines in the diagram. b. Name the intersection of WY and XZ. b. Name the intersection of planes N and S. 2. Identify the angle pair as only adjacent, not adjacent, or a linear pair. a. 1 and 2 b. 1 and 5 c. 5 and 4 3. Write a conditional statement ( If.., then ) from the sentence: A whole number is an integer. If, then. 4. Determine if the conditional statement is true. If false, give a counterexample. Conditional: If an angle is acute, then it has a measure of 30. True/False? If false, give counterexample: 5. Identify the hypothesis and conclusion of the conditional statement: If an angle is obtuse, then it measures 107. Hypothesis: Conclusion: 6. Write the converse of the following conditional statement. Then state its truth value. Conditional: If a number is even, then it is divisible by 4. False (2 is even but not divisible by 4.) Converse: 7. Find the coordinates of the midpoint of XY with endpoints X( 4, 6) and Y(3, 8). 8. Use the distance formula to find the distance between the two points F(4, 3) and G( 3, 2). For #9 10, Find the slope of each line. Then determine if the lines are parallel, perpendicular, or neither. Recall: lines have same slope & lines have opposite reciprocal slopes. 9. EF& GH for E( 2,3), F(6,1), G(6,4), H(2,5) 10. ST & VW for S(0,3), T(0,7), V(2,3), W(5,3) 11. Find the slope of each line. a. l b. m c. n

2 12. Write the equation of a line in slope intercept form that passes through (3, 8) and ( 3, 4). Hint: Find the slope first. Slope intercept form is y = mx + b, but you could start with point-slope form: y y 1 = m(x x 1 ) and simplify. 13. Write the equation of the line in point-slope form that passes through ( 5, 4) and has a slope of Write the equation of each line. a. b. c. 15. Simplify. a b c State the name for a polygon with the given number of sides. 3 sides 6 sides 9 sides 4 sides 7 sides 10 sides 5 sides 8 sides 12 sides 17. Using the diagram at the right, give an example of each type of angle pair. a. alternate interior angles and b. alternate exterior angles and c. corresponding angles and d. same side interior angles and e. vertical angles and f. linear pair and 18. Solve for x in each diagram. Show your work. a. b. c. 19. Classify each triangle by its angle measures. a. ACD b. ABD c. ADE 20. Classify each triangle by its side lengths. a. PQR b. PRS c. PQS

3 21. Given: PQR STU a. Find the value of y. b. Find PQ. 22. Find each measure. Show your work. a. m C b. ST c. AC d. GH & KH are tangent to 23. Identify the property that justifies each statement. both tangent to the circle. a. m XYZ m PQR, so m PQR m XYZ b. AB AB c. 4 A and A 1. So 4 1 G n + 3 8x 6 F H K The two segments are 5x 2n - 1 F. Find KH. 24. Complete the two-column proof. Given: m 1 m Prove: 1 4 Proof: Statements Reasons 25. Determine why the pair of triangles are congruent. a. b. c. d. 26. Complete the proof.

4 27. Determine if the figure is a polygon. If it is a polygon, name it by its number of sides. a. b. 28. Find each sum or measure. a. Find the sum of the interior angles of a convex dodecagon. b. Find the sum of the interior angles of a convex 16-gon. c. Find the sum of the exterior angles of a regular heptagon. d. Find the measure of each interior angle in a regular decagon. e. Find the measure of each exterior angle of a regular pentagon. 29. A park in the shape of quadrilateral PQRS is bordered by four sidewalks. Find the measure of each exterior angle of the park. 30. WXYZ is a parallelogram. Find each measure. a. b. m W YZ 31. Identify the most specific name for each quadrilateral. a. b. c. d. e. 32. GHJK is a rhombus. Find each measure. a. Find HJ b. Find b if m JLH 4b 6 and m JKH 2b Find m R.

5 34. Determine whether the two rectangles are similar. If so, write the similarity ratio and similarity statement. 35. An artist drew a picture of railroad tracks such that the ties, GH, and JK are parallel. Find the length of FH. EF 36. A geologist wants to measure the length of XY of a rock formation. To do so, she locates points U, V, X, Y, and Z as shown. a. Find ZV. b. Find XY. 37. Find the length of each segment. a. ST b. RS A student who is 5 ft 3 in. tall measured her shadow and the shadow cast by a water tower shaped like a golf ball. Find the height of the tower. 39. Find the distance across the pond, XZ. 40. Find the missing side length. Does this form a Pythagorean Triple? 41. Determine whether the side lengths form a triangle. If so, classify the triangle as acute, obtuse, or right. Show your work. a. 10, 12, and 16 b. 40, 41, 9 c. 4, 8, 3 d. 9, 4, Use a special right triangle to find the exact value of cos30 expressed as a simplified fraction.

6 43. Find the values of the variables. Give answers in simplest radical form. a. b. Find each length. Round to the nearest hundredth. 44. QR 45. LM Solve each triangle. Round lengths to the nearest hundredth & angle measures to the nearest degree. 46. HJ 47. C a B m A 31 b 10 m H A a m J b 48. The wheelchair ramp at the entrance of the Mission Bay Library has a slope of What angle does the ramp make with the sidewalk? Round to the nearest degree. 49. When the angle of elevation of the sun is 78, a building casts a shadow that is 6 m long. Find the height of the building to the nearest tenth of a meter. 50. Find each measure. 51. Find each measure. a. mbc a. m BAC b. mbed b. mcd 52. As part of an art project, Adam buys a circular piece of fabric and cuts out the sector shown. Find the area of the sector to the nearest tenth.

7 53. Find m RST 54. Find m AEC Find the value of x x 30 (2x 3) 57. Write the equation of P. 58. Find the equation of a circle whose center is at ( 1, 5) and whose diameter is Find the length of AB. Show your work. O A 10 ft 140 B 60. Find the area and perimeter of each figure. a. A = b. A = P = P = 61. Find the circumference and area of a circle with a radius of 6 m. Leave answer in terms of. C = A = Find the exact area of each figure. 62. parallelogram equilateral triangle Two similar rectangles have heights of 12 in. and 15 in. If the area of the smaller rectangle is 64 in 2, find the area of the larger rectangle.

8 69. Find the shaded area. 70. Describe the 3D figure that 71. Describe the can be made from the net. cross section. Find the surface area of each solid. Round to the nearest tenth a right cone with diameter 30 in. & height 8 in. Find the volume of each solid. Round to the nearest tenth, if necessary Find the volume of a cylinder with radius 8 yd and height 14 yd. Round to the nearest tenth. 77. Find the exact surface area and volume of a sphere with diameter 20 inches. SA = V = 78. In a cafeteria there are 4 choices for a main dish, 4 choices for a side dish, 5 choices of drinks, and 2 choices for dessert. Find the number of possible meals at the cafeteria. 79. Use the spinner to find the probability of each event. 80. Find the probability that a point a. P(pointer lands on red) chosen at random inside the circle lies in the shaded region. b. P(pointer lands on yellow or blue) 81. Identify the type of transformation. a. b. c. d. 82. Use point R with coordinates (3, 1) to perform each transformation. a. R is rotated 270 counterclockwise. b. R is translated along the vector 2, 3. State the coordinates for R. State the coordinates of R".