Geometry Honors Review for Midterm Exam

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1 Geometry Honors Review for Midterm Exam Format of Midterm Exam: Scantron Sheet: Always/Sometimes/Never and Multiple Choice 40 1 point each = 40 pts. Free Response: Show all work and write answers on the line 18 1, 2, 3 or 4 points each = 40 pts. Proofs: 2-column proofs. 2 Proofs at 10 points each = 20 pts. 100 points total

2 Proof Practice! Write a 2-column deductive proof for # Given: X is the midpoint of GE and DF Prove: DEF FGD Statements Reasons

3 2. Given: AX is an altitude and a median of DAB Prove: ABC ADC Statements Reasons

4 3. Given: ABC is isosceles with AD bisecting the vertex A Prove: BD CD and AD is an altitude of ABC Statements Reasons

5 4. Given: 1 2; 3 4 Prove: ST = PT Statements Reasons

6 5. Given: FS = DG; UD SE, UD = SE Prove: m 2 = m 6 Statements Reasons

7 True/False Practice: Write True or False on the line next to each statement. (hint! Good practice for A/S/N Questions!) 1. Two lines parallel to the same line must be parallel. 2. A line parallel to a plane is parallel to every line in the plane. 3. Two lines perpendicular to the same line must be parallel. 4. In a plane, two lines perpendicular to the same line must be parallel. 5. Two lines which lie in parallel planes must be skew. 6. In a plane, if a line intersects one of two parallel lines, then it must intersect the other. 7. Two points can lie in each of two different lines. 8. Three noncollinear points can lie in each of two different planes. 9. Three collinear points lie in only one plane. 10. Two intersecting lines are contained in exactly one plane. 11. If two lines intersect, then they intersect in exactly one point. 12. If two planes intersect, then their intersection is a line. 13. The diagonals of a parallelogram are congruent. 14. Each interior angle of a regular pentagon is 120º. 15. An equiangular quadrilateral cannot be equilateral. 16. The diagonals of an isosceles trapezoid are congruent.

8 Multiple Choice Practice: Circle the letter of the correct answer. 17. A and B are regular polygons and A has 2 more sides than B. The measure of each interior angle of A is 6 greater than the measure of each interior angle of B. How many sides does A have? a. 6 b. 8 c. 10 d Planes K and J are parallel. Line p lies in plane K and line q lies in plane J. Which of the following statements must be true? a. p and q are always parallel b. p and q are sometimes parallel c. p and q are never parallel d. p and q are always coplanar e. p and q sometimes intersect 19. AD DC, AB DC, DE bisects ADC and m ECB = 40. Find m DEC. a. 90 b. 95 c. 85 d. cannot be determined 20. Find m ABC if m A = 48 and m C = 46. a. 94 b. 86 c. 84 d. cannot be determined 21. Find m ADC. a. 53 b. 43 c. 137 d In the figure, m ABE = m EDF = m BEC. Which of the following pairs of lines must be parallel? I. AB and CD II. BE and DF III. AE and CF a. I only b. II only c. III only d. I and II only e. I and III only

9 23. In ABC, BD and CD are angle bisectors, and CE BD. If m BAC = 70, what is m DCE? a. 70 b. 105 c. 125 d Use the diagram to the right for # If r s, then 1? a. 9 b. 11 c. 5 d. 9 and If 11 14, then? a. b c b. r s c. b c and r s d. none of these 26. If 3 12, then? a. b c b. r s c. b c and r s d. none of these 27. If b c, then 6 must be to 3? a. congruent b. supplementary c. congruent and supplementary d. adjacent e. congruent and adjacent 28. If two angles of a triangle measure 47 and 93, then the measure of the third angle is? a. 46 b. 30 c. 50 d. 60 e. none of these 29. The sum of the measures of the exterior angles, one at each vertex, of a convex octagon is? a. 135 b c. 45 d. 360 e. none of these

10 30. Find the measure of each interior angle of a regular polygon with 10 sides. a. 144 b. 180 c. 36 d. 360 e. none of these For examples 31 34, circle the postulate or theorem that justifies the conclusion. 31. If AX BC and X is the midpoint of BC, then ABX ACX. a. SSS b. SAS c. ASA d. AAS e. HL 32. If AX BC and AX bisects BAC, then ABX ACX. For #31-32 a. SSS b. SAS c. ASA d. AAS e. HL 33. If GH = GK and HJ = KJ, then JHG JKG. a. SSS b. SAS c. ASA d. AAS e. HL 34. If GH HJ, GK KJ, and GH = GK, then GHJ = GKJ. For ex a. SSS b. SAS c. ASA d. AAS e. HL 35. Which of the following statements is equivalent to the statement p implies q? a. q implies p b. If p, then q. c. q only if p. d. p if q. 36. The measure of the supplement of an angle is 14 less than 3 times the measure of the complement. Find the measure of the complement. a. 38 b. 52 c. 142 d Which of these is true? I. m 1 = m 3 + m 4 II. m 1 > m 2 III. m 1 > m 3 a. I and II only b. II and III only c. I and III only d. I, II and III

11 38. Which of the following triangles does not exist? I. acute isosceles II. Right scalene III. obtuse equilateral IV. obtuse scalene a. I only b. II only c. III only d. II and III e. II, III, IV 39. Points A, B, C, and D are coplanar. A, B, and C are collinear but B, C, and D are not. How many different lines are determined by points A, B, C, and D? a. 3 b. 4 c. infinitely many d. cannot be determined 40. j and k are intersecting lines. A and B are points on j, and C and D are points on k. How many planes contain points A, B, C, and D? a. none b. exactly one c. infinitely many d. cannot be determined 41. Points M, A, T, H, and P are arranged on a line so that T is the midpoint of HM, M is the midpoint of HA, and P is the midpoint of AT. Which of the following are true? I. P is on MA. II. M is on TH. III. PH = TA a. I only b. II only c. III only d. I and II only e. II and III only 42. In the figure, AC = 24, AB = 6x 6, BC = 5x 3, and BE = 3x +2. Which do you know is true? I. AC bisects DE II. DE bisects AC III. DE bisects AC a. I only b. II only c. III only d. I and II only e. II and III only 43. Find the values of x and y. (The figure is not drawn to scale.) a. x = 20, y = 34 b. x = 10, y = 52 c. x = 12, y = 18 d. x = 11, y = Which of the following is the hypothesis of the given conditional? If I win, then I ll stay. a. I ll stay. b. I win. c. If I stay, I won. d. I ll leave if I lose. e. I ll win if I stay.

12 45. Point A lies in plane K, but point B does not. A line l through B intersects K at point C. Which of the following must be true? I. A, B, and C are coplanar. II. The midpoint of AB lies in plane K. III. The midpoint of AC lies in plane K. a. I only b. II only c. III only d. I and II only e. I and III only 46. In the figure, BD bisects ABE, BE bisects ABG, m EBF = 37, and m CBG = 44. Find m DBF. (The figure is not drawn to scale.) a. 68 b. 34 c. 82 d Which of the following expressions represents the average of x and z? a. 180º - y b. 90º - y c. 180º - 2y d. 90º - 2y e. y 48. In PQR: P is equidistant from A and C, Q is equidistant from A and B, R is equidistant from B and C. If the perimeter of PQR is 24 and AQ = 3, find PR. a. 9 b. 10 c. 12 d. 15 e The measure of AEC = 150. The measure of DEB = 138. Find the measure of BEC. a. 72 b. 90 c. 96 d. 108 e. 120

13 50. Find x. a. 40º b. 50º c. 60º d. 70º e. 80º 51. If 1 is supplementary to 2, 3 is supplementary to 4, and 2 4, then: a. 1 3 b. 1 2 c. 1 4 d. 1 is supplementary to 3 e. 2 is supplementary to In the diagram, AB DE and A D. In order to conclude that ABC DEF by SAS, it is necessary to know that: a. B E b. ACB DFE c. AC DF d. BC EF e. BF CE 53. Which of the following does not determine a plane? a. two parallel lines b. three non-collinear points c. a line and a point not on the line d. two perpendicular lines e. none of the above (they each determine a plane) 54. Each interior angle of a polygon has a measure of 160. The number of sides in the polygon is: a. 9 b. 12 c. 18 d. 20 e. none of these 55. If the measure of an angle exceeds its supplement by 20, then the measure of the angle is: a. 100 b. 80 c. 55 d. 35 e In order to prove that a point lies on the perpendicular bisector of a segment, it is necessary to show: a. the point is on the segment b. the distances from the point to the endpoints of the segment are equal c. the point is the midpoint of the segment d. the point is the perpendicular bisector of the segment e. all of these

14 57. If two angles are congruent and supplementary, the angles must be: a. adjacent angles b. acute angles c. obtuse angles d. straight angles e. right angles 58. If the vertex angle of an isosceles triangle is 40º, then each base angle is: a. 70º b. 140º c. 40º d. 20º e. 50º 59. The altitudes of an equilateral triangle are a. medians b. congruent c. angle bisectors d. all of these 60. In PQR, m QRS = 2x + 20, m P = 50, and m Q = x +20. Find m QRP. a. 50 b. 60 c. 70 d A polygon with six sides is called a a. hexagon b. heptagon c. octagon d. none of these 62. If the sum of the measures of the interior angles of a polygon is 540º, how many sides does the polygon have? a. 4 b. 5 c. 6 d. none of these 63. If a parallelogram has congruent diagonals, then it is a a. trapezoid b. rhombus c. rectangle d. none of these 64. In trapezoid ABCD, EF is the median, DC = 9, and EF = 12. Find AB. a b. 15 c. 21 d. none of these

15 65. In isosceles trapezoid ABCD, AD BC. If m A = x, then m c =? a x b. 2x c. 180 x d. none of these 66. In the figure, the measure of Y is a. 25º b. 70º c. 110º d. none of these 67. The diagonals of a square a. are congruent b. bisect each other c. are perpendicular d. all of these 68. If 2y = 7x, then the ratio of y to x is a. 7 2 b. 2 7 c. y x d. none of these 69. If 5 4 = x 9, then x is equal to a. 7.2 b c. 45 d. none of these 70. How many sides does a regular polygon have if the measure of each interior angle is 150º? a. 8 b. 12 c. 15 d. none of these 71. Which of these is true about an altitude of a triangle? a. It can be in the interior of the triangle. b. It can be in the exterior of the triangle c. It can be a side of the triangle d. All of these are true e. None of these are true 72. If the measures of two remote interior angles of a triangle are 51º and 46º, then the measure of their corresponding exterior angle is a. 5º b. 46º c. 51º d. 97º e. none of these

16 73. Based on the markings shown, which of these is a true statement? a. IG is a median of FHI b. CE is an altitude of ABC c. IH is an altitude of FHI d. none of these e. all of these 74. Given: Isosceles ABC with AC BC, m A 5x 6, and m C 6x 8. Which of the following is true? a. m A = 56 b. m B = 56 c. m C = 68 d. all of these e. none of these For #75 76, use the figure: 75. Which figure shown is a polygon? a. 2 b. 3 c. 4 d. all of these e. none of these 76. Which figure shown is convex? a. 1 b. 2 c. 3 d. 4 e. none of these 77 If ABCD is a parallelogram, which of the following can be proved? a. AC BD b. AC BD c. AB BC d. all of these e. none of these 78. Given: Trapezoid ABCD with diagonals AC and BD. Which of the following can be proved? a. AC BD b. AC and BD bisect each other c. AC BD d. all of these e. none of these

17 79. If ABC ~ DEF, AB = 8, BC = 10, CA = 12, and DE = 12, then: (hint-draw a diagram!) a. EF = 10 b. DF = 15 c. EF = 5 d. C F e. none of these Fill in the blank with sometimes, always, or never to make each statement true. 80. A median of a triangle bisects the opposite side of the triangle. 81. The complement of an acute angle is an obtuse angle. 82. If AB is the perpendicular bisector of CD, then CD is the perpendicular bisector of AB. 83. Two lines perpendicular to the same plane are perpendicular to each other. 84. The bisector or an angle of a triangle bisects the side opposite the angle. 85. If two triangles have all their corresponding angles congruent, then their corresponding sides are congruent. 86. The angle bisector of the largest angle of a triangle with sides of 8, 12, and 16 divides the opposite side into 2 segments with measures of and. (hint: draw a diagram!) 87. The measure of the largest angle of a triangle is three times the measure of the smallest angle and 30 more than the measure of the third angle. Find the measure of the largest angle. 88. State which triangles are similar, and write the postulate or theorem that justifies your answer.

18 89. Given: DE AB, DC = 5, DA = 7, and AB = 10. Find DE. 90. Given: DEF with H the midpoint of DE, FG = 9, FE = 18, and FD = 14. Find GH. 91. Given: Trapezoid ABCD with AB = 19 and DC = 10. Find the length of the median. 92. Given: Parallelogram ABCD with m A = 5x 3, m D = 7x + 3. Find m A. 93. The perimeter of a triangle is 320 cm and its sides are in the ratio 3:5:8. What are the lengths of the sides of the triangle?

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