VIEWS: 23 PAGES: 14 POSTED ON: 12/4/2011 Public Domain
Name _____________________________ Date ___________________ Review ~ Pre AP Geometry Midterm 2010 Vocabulary is on the test, you need to know all, so if you see one you don’t remember or think you need review on, especially formulas, postulates or theorems we haven’t seen in a while, please make sure to review the concept. Vocabulary: Undefined terms Conditional statement Scalene triangle Point Converse Isosceles triangle Line Inverse Triangle sum theorem Plane Contrapositive Exterior angle theorem Collinear Hypothesis Third angles theorem Coplanar Conclusion CPCTC Noncollinear Law of detachment SSS Noncoplanar Law of syllogism SAS Segment Biconditional statement ASA Endpoint Postulate AAS Ray Theorem HL Opposite rays Counterexample Included side / angle Postulate Algebraic properties Isosceles triangle Postulates (chapter 1) from chapter 2 properties/theorems Distance formula Proof Perpendicular bisectors Congruent Two column proof Angle bisectors Midpoint (definition Parallel lines (and it’s Medians and formula) slope) Altitudes Bisect Perpendicular lines Circumcenter Segment bisector (slope) Incenter Segment addition Skew lines Centroid postulate Transversal Orthocenter Angle addition Corresponding angles Triangle midsegment postulate Alternate interior angles theorem Angle Alternate exterior Equidistant Vertex angles Point of concurrency Acute angle / triangle Same side interior Triangle inequality Right angle / triangle angles theorem Obtuse angle / triangle Slope (formula) Hinge theorem and it’s Straight angle Coinciding lines converse Angle bisector Point slope form Pythagorean theorem Adjacent angles Slope intercept form Converse of the Linear pair Vertical lines (equation Pythagorean theorem Complementary angles and it’s slope) Pythagorean triple Supplementary angles Horizontal lines 45-45-90 Vertical angles (equation and it’s slope) 30-60-90 Inductive reasoning Equiangular triangle Angle side relationships Deductive reasoning Equilateral triangle in triangles pg 333 Refer to the figure below to name each of the following. Use appropriate symbols where necessary. 1.__________ The intersection of M and L. L 2.__________ A ray opposite DB. B 3.__________ A plane containing CE. C E 4.__________ The intersection of L and CE. M D 5. _________ Three collinear points A 6. _________ Three coplanar points ____ 7. Find AC. A B C D –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 ____ 8. D is between C and E. = , = , and DE = 27. Find CE. C 4x + 8 D 27 E 6x ____ 9. B is between A and C. AC = 24 and BC = 11. Find AB. L _____ 10. What are three names for the angle? 1 N M ______11. If and then what is the measure of The diagram is not to scale. mWXY 88 ; mWXZ 4 x 3 ; mZXY 2 x 1 ______ 12. Solve for x: W Z X _____ 13. Find the measures of two complementary angles, A & B, if mA = (7x + 4)Y mB = (4x + 9). and _____ 14. Find the distance between the points E(-3, -4) and F(5, 4). Simplify the radical if necessary. _____ 15. Find the midpoint of the segment with the given endpoints. (-7, 7) and (-9, 8) _____ 16. The complement of a 35 angle is an angle with a measure of: _____ 17. The supplement of a 25 angle is an angle with a measure of: In the diagram, name the / a pair of ________18. adjacent angles. ________19. Name a linear pair: 1 2 3 ________20. Vertical angles 5 4 _____ 21. M is the midpoint of AB. AM = 9x – 6 and BM = 6x + 27 Find: X= AM = BM = _______22. bisects and Solve for x and find The diagram is not to scale. 23. How a line and a line are segment the same? How are they different? _______________________________________________________________________ 24. How are angles classified? Give an example of each. ________________________________________________________________________ 25. What are the building blocks of geometry? ________________________________________________________________________ 26. How are Supplementary angles and a linear pair the same? Different? ________________________________________________________________________ Draw, label and show the notation for each of the following: 27. A line segment with endpoints C and D. 28. A line containing X and Y 29. A ray with endpoint M that passes through P. Given the diagram: 30) Name the type of angles: __________________________ y bx 26g 2 bx 14g 5 31) Solve for x and y KNOW: All Properties of equality and congruence pgs 104 and 106. 32. Conditionals are known as ______________________________________. 33. What is a conjecture? _____________________________________ 34. Inductive reasoning is based on __________________________ and deductive reasoning is __________________________________________________. 35. A counterexample invalidates a statement. TRUE FALSE 36. Write the negation of: Points on the same plane are coplanar. _____________________________________________________ 37. When a conditional and its converse are true you can combine them as a ______________________________. Write a conditional statement for the situation described, then write its converse, inverse, and contrapositive. Parallel lines do not intersect. Underline the hypothesis once, and the conclusion twice. 38. Conditional: 39. Converse: 40. Inverse: 41. Contrapositive: If possible, write the biconditional statement, if not tell why. 41. Every isosceles triangle has two congruent sides. 42. Use the Law of Syllogism to draw a conclusion from the two given statements. If you exercise regularly, you have a healthy body. If you have a healthy body, you have more energy. ______________________________________________________________________ ______________________________________________________________________ 43. Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible. I will score well on the exam if I study for 1 hour each day. I will score well on the exam. ______________________________________________________________________ 44. Find the missing elements in the sequence below. 2, 5, 10, 17, 26, 37 , , 65, 82 , , 122, . . . 45. Find the values of x and y. 46. Identify the transversal and classify the angle pair and . n m 3y° 2 126° 1 3 3x – 6° 4 9 10 5 6 12 11 Drawing not to scale l 8 7 Name the indicate angles 1 8 47. 4 and 5_____________ 2 7 48. 2 and 3_____________ 49. 1 and 7_____________ 3 6 50. 6 and 8_____________ 4 5 51. 1 and 5_____________ 52. 2 and 6_____________ . If p q , then find the value of x. 53. 54. (4x) p (6x) p q (3x) q (2x + 30) 55. Name all the angles if m5 = 120 56. Find the values of x and y. The diagram is not to scale. 1 2 p 4 3 41° (x – 3)° (y + 8)° 56 74° q 7 8 pq Determine whether and are parallel, perpendicular, or neither. 57. Write the equation of a line that has: 58. slope –2; passes through ( 3, 5 ) __________________________________ 59. Find the slope of line given these two points (0, 7), (1, 9). _____________________ And write the equation of the line: ________________________ 60. Graph 3x – 7y = 14 61. Graph y = -9 Write equations for the line that are parallel and perpendicular to the given line and that passes through the given point. 3 62. y = x – 9; (–8, –18) 4 63. Know how to classify triangles by sides and by angles: 40 64.x = _______ 65.x= ________ x x 155 52 35 38° 66.x=______ 67. x=______ 80 y= ______ 19° z=______ (3x -22) 56° x x° z° y° 68. In the diagram: C D List the six congruent parts: F A B E 69. Write a congruence statement for the given triangles. ___________________________________ 70. ADC BDC by: _______ 71. These triangles are congruent by: _________ Finish the congruence statement: C A D B 72. These triangles are congruent by: _______ 73. These triangles are congruent by: _______ 74. These triangles are congruent by: _______ 75. These triangles are congruent by: _______ 76. What is the difference between ASA and AAS? __________________________ 77. What does CPCTC stand for? ________________________________________________________________________________________________________________ 78. If BCDE is congruent to OPQR, then is congruent to 79. One of the acute angles in a right triangle has a measure of . What is the measure of the other acute angle? 80. Use the information in the figure. Find 81. Find m , given , , and m . B E E | A D C F | 116° D F Drawing not to scale Determine whether the given measures can be the lengths of the sides of a triangle. Write yes or no. And if so what kind of triangle. Explain. 82. 3, 9, 10 83. 40, 9 , 41 84. 4, 8, 14 85. 7, 20, 23 86. Determine whether the set of numbers can be the measures of the sides of a right triangle. Then state whether they form a Pythagorean Triple. 10, 24, 26 Simplify the radical expression. 87. 88. 89. 8 3 75 90. 3 (4 5 6 3 ) Simplify the radical expression by rationalizing the denominator. 91. 92. 93. 94. Find x. 95. Find n. 6 37 x 6 2 n 15 96.Find the value of x. The diagram is not to scale. 97.List the sides in order from shortest to longest. The diagram is not to scale. J 40 66° 50° K x 40 32 64° 25 25 L 98. Find the values of x, y, and z. 99. Find x and y. K N y 29° 31° 3 in. 45° J x M 62° x y z M P O 100. The hypotenuse of an isosceles right triangle is 6 inches. Find the area. 101. Find the values of x and y. 102. Find y. N N x 22 mm y 45° 30° 45° M y P M 5 ft P 103. Find x and y. Write all radicals in simplest form. 104. What is the perimeter and area of the triangle? (Round to the nearest decimal place.) N C x y 6 in. 30 A 6 3 ft B 30 M L 105. Points B, D, and F are midpoints of the sides of EC = 39 and DF = 17. Find AC. The diagram is not to scale. A B F C D E 106. For a triangle, list the respective names of the points of concurrency of • perpendicular bisectors of the sides • bisectors of the angles • medians • lines containing the altitudes 107. In ABC, G is the centroid and BE = 9. Find BG and 108. GE. C C X Z B D G A Y B Name an altitude in the given triangle. A F E _______________ Name a median in the given triangle. _______________ 109. Find the length of , given that is a median of the triangle and AC = 40. D A B C 109. R X S T If X is the midpoint of , then is called a(n) ________________ of . If TX is on the perpendicular bisector of , then TX is equidistant from _____ and _____. If , then is called a(n) ________________ of . If is the bisector of then ______ ______ A Proofs: 3 4 1. Given: AB AC, X is the midpoint of BC Prove: ABX ACX 1 2 B X Proof: C Statements Reasons 2. Given: Given B is in the interior of AOC (2x)° and Prove: m BOC = 108 6(x – 3)° Drawing not to scale Proof: Statements Reasons A 3 4 3. Given: AX BC, X is the midpoint of BC Prove: ABX ACX 1 2 B Proof: X C Statements Reasons 4. Given: AB II DE, AB DE Prove: ABC EDC Proof: Statements Reasons B 5. Given: DCA BCA, B D Prove: AB AD C A Proof: D Statements Reasons q 1 2 6. State the reasons in this proof. 3 4 p Given: 5 6 r Prove: 7 8 Proof: Statements Reasons 1 3 l 7. Given: Prove: 2 m Proof: Statements Reasons B C A 8. Given: Prove: D Proof: Statements Reasons 9. Given: B and D are right angles, C is the midpoint of AE Prove: C is the midpoint of BD Proof: Statements Reasons A 10. Given: 1 2, X is the midpoint of BC 3 4 Prove: AX bisects BAC Proof: 1 2 Statements Reasons B X C B 11. Given: ABC is isosceles, with base AC, FGD IHD, BD AC Prove: AEC is isosceles Proof: A D C Statements Reasons