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Geometry Midterm Review Name: ___________________________ Period: ____ Date: ___________ 1) Ray PR is shown in which sketch? a) b) c) P Q R d) R P P Q R Q Q R P 2) If RS = 32.2 and QS = 62.8, find QR. a) 95 R Q b) 32.2 c) 30.6 S d) 20.6 3) Use the Segment Addition Postulate to solve for p. FE = 4p + 20 F EG = 5p + 16 E G FG = 45 a) p = 1 b) p = 4 c) p = 5 d) p = 6 4) Find the distance between A(6, 0) and B(4, 4). a) 116 b) c) 20 116 d) 20 5) Find the midpoint of A(6, 0) and B(4, 4). a) (1, 2) c) (8, 4) b) (5, 2) d) (2, 8) 6) M is the midpoint of segment AB. Given the coordinates of A(2, 4) and M(4, 6), find the coordinates of B. a) (3, 1) b) (6, 16) c) (6, 8) d) (6, 2) 7) Which of the following angles measures 125? a) b) c) d) 8) If mJOL = 50 and mKOL = 27, then what is the measure of JOK? a) 25 b) 23 c) 28 d) 20 J K O L 9) Given that mGED=60, mGEF=2x + 7 and mDEF=7x – 1, find mGEF and mDEF. a) b) c) d) G mGEF = 41 and mDEF = 19 mGEF = 47 and mDEF = 13 mGEF = 13 and mDEF = 47 mGEF = 19 and mDEF = 41 F E D 10) In the figure below, mAED = 128. Which of the following statements is false? a) b) c) d) E B 11) 1 and 2 are ______. a) b) c) d) 1 a linear pair complementary angles supplementary angles vertical angles 2 12) Find the measure of 1. a) b) c) d) 42 48 58 138 42 1 13) Solve for x. a) b) c) d) 5x + 137 0 1 2 5 4x + 25 14) Solve for x. a) b) c) d) 1 2 3 6 5x + 24 3x + 30 15) Name an angle that is adjacent to BOC a) b) c) d) DOE AOE DOB BOA D A mBEC = 128 AEB and DEC are congruent BEC and CED are vertical angles mAEB = 52 B C A O E D C 16) Using the diagram, name an angle that is complementary to COD. a) AOE b) BOC c) DOE B d) AOC C A O 17) Rewrite the statement in if-then form: Vertical angles are congruent. a) b) c) d) E If angles are congruent then they are vertical angles. If vertical angles are congruent then they can be measured. Angles are vertical angles if and only if they are congruent. If angles are vertical angles then they are congruent. 18) What is the converse of the statement, “If it rains then I carry my umbrella.”? a) b) c) d) “If it does not rain, then I do not carry my umbrella.” “If I do not carry my umbrella, then it does not rain.” “If I do not carry my umbrella, then I will get wet.” “If I carry my umbrella, then it rains.” 19) “If I get a chance then I will succeed.” In this conditional statement, the underlined portion is a) the hypothesis b) the argument c) the conclusion d) the converse 20) What is the inverse of the statement, “If two lines are parallel, then they do not intersect.”? a) b) c) d) “If two lines are not parallel then they intersect.’ “If two lines intersect then they are not parallel.” “If two lines do not intersect then they may be skew.” “If two lines do not intersect then they are not parallel.” 21) Which of the following statements is false? a) b) c) d) Three non-collinear points determine a plane. Any three points are collinear. A line contains at least two points. Through any two distinct points there exists exactly one line. 22) State a counterexample to the following statement: a) b) c) d) “If x2 = 25, then x = 5.” x=5 x = 5 x2 = 25 x 2 = 100 23) The figure at right represents which of the following statements? C a) b) c) d) two perpendicular rays two perpendicular lines a straight angle AB = AC A B D 24) Identify this property of congruence: a) Transitive CD CD b) Reflexive c) Symmetric d) Substitution B 26) In the cube shown at right, AD and HG are called _____ a) b) c) d) C A parallel lines perpendicular lines intersecting lines skew lines D F G E H n 27) In the figure shown, 1 and 2 are ____ 2 a) b) c) d) same-side interior angles corresponding angles alternate interior angles alternate exterior angles m 1 28) In the figure, 6 and 3 are _____ A) B) C) D) l n corresponding angles alternate interior angles alternate exterior angles consecutive interior angles 1 2 4 5 8 l 3 6 m 7 29) In the figure above, 6 and 2 are ____ a) alternate interior angles c) corresponding angles b) alternate exterior angles d) same-side interior angles 79 P 30) Find m1, given that PQ || RS a) 11 b) 79 c) 91 1 R S d) 101 31) In the figure, l n and r is a transversal. r Which of the following is not necessarily true? a) b) c) d) 2 6 8 2 7 4 5 3 Q 1 4 6 5 8 7 2 l 3 n 32) In the figure shown, HC GD , and mABC = 108. C Which of the following statements is false? a) b) c) d) D mDEF = 72 ABH and AEG are alternate exterior angles HBF and AED are alternate interior angles mGEF = 108 A E B F H G 33) Find the slope of the line passing through the points (1, 6) and (6, 5). a) 7 b) y 34) A line parallel to a) y 1 7 11 5 c) d) 7 2 x 7 is: 3 2 x7 3 b) y 3 x7 2 c) y 3 x2 2 d) y 2 x 1 3 35) Which describes the relationship between the lines with equations 7 x 6 y 4 and 6 x 7 y 0 ? a) parallel b) same line c) perpendicular d) neither parallel nor perpendicular O 36) Classify NOP. 8 9 a) Equilateral b) Isosceles c) Scalene d) none of these N 10 P B 37) Name an obtuse triangle in the diagram at right. a) ADB b) BDC c) ABC 35 55 d) none of these 65 D 30 A 38) Find the value of x. a) 80 b) 100 60 C x c) 160 d) 170 10 39) Solve for x. a) 45 x - 10 2x b) 55 c) 90 d) 145 55 40) Which figures appear to be congruent? a) b) c) d) 3 and 4 1, 2, and 4 2 and 5 1 and 4 1 3 2 4 5 41) If ABC XYZ, then AC ______. a) XY b) YZ c) XZ d) AX 42) If JKL STU, JK = 10 feet, mK = 59, and mU = 21, which of the following is false? a) JL = SU b) KL = TU d) K S c) mS = 100 B 43) In the diagram, B E and C F. Find the value of x. A a) 25 b) 35 c) 50 d) 75 35 x + 50 D C F 75 E B 44) What must be true for ABC EDC by SAS? a) B D c) AC CE E b) AB DE d) A E C A D 45) Which of the following statements must be true, if AD BC and AB = AC? a) b) c) d) A ABD ACD by SSS ABD ACD by SAS ABD ACD by HL There are no congruent triangles B a) EDC c) ACE D B 46) Refer to the figure at right. ABC _____ C D C b) EDA d) CDE A E A 47) Using just the information shown in the diagram, which postulate or theorem can be used to prove that ABC EDC? a) SSA c) AAS b) SSS d) SAS C D B E 48) What is the measure of each base angle of an isosceles triangle if its vertex angle measures 32 and its 2 congruent sides measure 17 inches? a) 32 b) 58 c) 74 d) 148 49) In ABC, if AB BC and mA = 39, then mC = ______. a) 39 b) 51 c) 102 d) 141 50) Compare and contrast vertical angles and linear pairs. 51) Find the values of x and y. a) x = 70 and y = 50 c) x = 40 and y = 70 x b) x = 40 and y = 110 d) x = 70 and y = 110 110 y 58) In the figure shown, mAED = 110. Which statement is false? a) b) c) d) A mAEB = 80 AEB and DEC are vertical angles BEC and CED are adjacent angles mBEC = 110 59) If line a is parallel to line b, what is m1? a) 40 c) 90 b) 50 d) 140 D E B C 1 40 60) Lines AB and CD intersect at P. PR is perpendicular to AB and mAPD = 170. What is the measure of DPB? a) b) c) d) 10 20 30 40 61) A ladder is leaning against a house at an angle of 38, as shown in the diagram. What is the measure of the angle x, that the ladder makes with the ground? a) b) c) d) 38 42 52 142 a b 62) Line a is parallel to line b if: a) m4 = m2 c) m4 = m5 2 1 b) m3 = m5 d) m3 = m2 3 a 4 5 6 7 8 b 63) ABC is a right triangle with right angle at C. Which are the possible measures of A and B? a) b) c) d) 48 and 50 38 and 32 52 and 38 52 and 128 64) Which conclusion follows logically from the true statements? “If negotiations fail, then the baseball strike will not end.” “If the baseball strike does not end, then the World Series will not be played.” a) b) c) d) If the baseball strike ends, the World Series will be played. If negotiations do not fail, the baseball strike will end. If negotiations fail, the World Series will not be played. If negotiations fail, the World Series will be played. 65) Given that AD BC and AC BD , which could be used to prove that DCA CDB? a) SSS c) ASA b) SAS d) AAS 66) On the shores of a river, surveyors marked locations A, B, and C. mACB = 70 and mABC = 65. Which lists the distances between these locations in order, least to greatest? a) b) c) d) AB, BC, AC BC, AB, AC BC, AC, AB AC, AB, BC B C A 67) The figure has angle measures as shown. What is mBCD? a) 120 c) 60 b) 80 d) 30 68) What is m3? a) 65 c) 85 b) 75 d) 90 3 65 150 69) Which of the following could be the lengths of the sides of ABC? a) b) c) d) AB = 12, BC = 15, AC = 2 AB = 9, BC = 15, CA = 4 AB = 150, BC = 100, CA = 50 AB = 10, BC = 8, AC = 12 70) To find the contrapositive of a conditional statement you should: a) b) c) d) Find the inverse of the converse of the original statement. Find the converse of the inverse of the original statement. Negate the hypothesis and conclusion of the converse of the original statement. All of the above. 71) Three lookout towers are located at points A, B, and C on a section of the national forest shown in the diagram. Which of the following is true concerning ABC formed by the towers? a) b) c) d) mA is greatest mC is greatest mA is least mC is least C 4123 km 5385 km B A 4472 km 72) What value of x will make lines l and m parallel? a) b) c) d) 25 30 40 60 2x + 30 4x - 90 C 73) In the figure, mCAD is twice mCAB. What is mCAB? a) b) c) d) 120 60 45 30 D 74) Triangle XYZ is a right triangle with the right angle at Z. Which are possible measures for angle X and angle Y? a) 40 and 42 c) 48 and 50 b) 44 and 46 d) 52 and 54 A B 75) Explain the difference between similar triangles and congruent triangles. Be specific. Questions 76-90: True/False. For the following questions, bubble “a” for true and “b” for false. 76) It is possible to have a triangle with side lengths 7, 7, and 9. a) True b) False 77) Corresponding parts of congruent triangles are equal in measure. a) True b) False 78) Coplanar points are collinear. a) True b) False 79) Collinear points are coplanar. a) True b) False 80) SSA is a method to prove triangle congruency. a) True b) False 81) When two planes intersect, they form a line. a) True b) False 82) Equilateral triangles are equiangular. a) True b) False 83) Skew lines are coplanar. a) True b) False 84) If two lines are parallel, they have the same slope. a) True b) False 85) A right triangle can have up to two right angles. a) True b) False 86) In a right triangle, the hypotenuse is adjacent to the right angle. a) True b) False 87) The slope of a horizontal line is zero. a) True b) False 88) The AAA method is used to prove that triangles are congruent. a) True b) False 89) A scalene triangle never has congruent sides. a) True b) False 90) The Symmetric Property states an object is equal to itself (ex. b = b). a) True b) False 8 in 2 ft 91. Simplify the following ratio as much as possible: a) 4 1 92) Solve the proportion: a) 3/10 b) 4 in 1 ft c) 8 24 d) 1 3 x2 1 10 2 b) 3 c) 4 d) 5 93) In the diagram ABC ~ XYZ. Find YZ. a) 9/2 b) 2 c) 5 d) 8 94) Let p represent “Line AB and line BC are perpendicular” and let q represent “ABC is a right angle”. Which represents the contrapositive of “If line AB and line BC are perpendicular, then ABC is a right angle”? a) q → b) q → c) ~q → d) ~q → p ~p p ~p 95) Are the two triangles in this diagram similar? If so, give the similarity statement. a) b) c) d) Yes, ABC ~ CDE Yes, ABD ~ EDC Yes, ABD ~ ECD No, the triangles are not similar. 96) In the diagram shown on the right, what is the length of AB ? a) 4 b) 3/2 c) 8/3 d) 16 97) If two sides of a triangle have lengths 7 and 11, which is a possible length for the third side of the triangle? a) b) c) d) 18 5 4 2 98) The coordinates of the midpoint of line segment CD are (4, -5) and the coordinates of C are (8, -8). What are the coordinates of D? a) b) c) d) (-2,0) (0,0) (0,-2) (2,-2) 99) If two triangles have one pair of congruent angles and if the lengths of the corresponding adjacent sides are proportional, then the triangles are: a) equal b) congruent c) similar d) obtuse