Geometry Midterm Review Mr. Pisciotta
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1 Geometry Midterm Review Mr. Pisciotta Chapter 1: Essentials of Geometry Sections Points, Lines and Planes 1.2 Use segments and Congruence 1.3 Midpoint and Distance Formulas -Be able to graph a line given an equation -Find the distance and midpoint between any two points on a line segment or graph 1.4 Measure and Classify Angles 1.5 Angle Pair Relationships a) Parallel lines cut by a transversal b) Angles created by a transversal 1.5 Constructions: a) Construct an angle bisector b) Construct a segment bisector DEFINITIONS: Congruent segments Congruent angles Midpoint Angle bisector Vertical angles
2 Complementary Supplementary Perpendicular lines Parallel lines POSTULATES: Point, Line and plane postulates (as covered in review) Segment addition Angle addition Linear Pair postulate PROPERTIES Multiplicative Inverse Reflexive a=a Symmetric a=b then b=a Transitive: if a = b and b = c, then a=c Substitution: If a = c, then a can be substituted for any value c Distributive: a(b+c)=ab+ac Chapter 2: Reasoning (logic) and Proof Sections 2.1, 2.2, Inductive Reasoning Analyze Conditional Statements a) converse b) inverse c) contrapositive
3 d) biconditional e) know the truth values (if p then q, etc ) 2.6 Algebraic Proofs a) formal two column proof b) Algebraic properties/definitions The following is intended to give the student an accurate idea of what type of skills are required for the midterm exam for Tuesday 12/13/16. The exam is worth a MINIMUM of 150 points and will replace a lower test grade. Be sure you can work all of the problems accurately. If not, ask for help! Choose the best answer for each question. 1. Find the length of the segment with endpoints L(-1, -3) and M(-6, 9). A. 13 B. 17 C. 5 D Points A, B and D A. determine a plane B. are collinear C. are contained in only plane P D. are noncoplanar points C B F G D A E P R 3. What is the intersection of planes P and R. A points A, D and B B. AB C. AB D. AD 4. What is the measure of QT if R is between Q and T, QR = 14 and RT = 5? A. 10 B. 11 C. 19 D Find the coordinates of the midpoint of the segment with endpoints D(6, 6) and E(-2, 2). A. (3, 4) B. (2, 4) C. (4, 8) D. (1, -1) 6. What are the sides of 5? A. WG and WF B. AB and WF C. WB and WG D. WB and WF 1 C E W 6 B F G A 7
4 7. 5 and 6 are A. adjacent B. vertical C. supplementary D. complementary 8. 8 and 9 are A. adjacent B. vertical C. supplementary D. complementary 9. 1 and 2 are A. adjacent B. vertical C. complementary D. linear pair and 4 are A. adjacent B. vertical C. linear pair D. complementary 11. Find m 1. A. 25 B x+10 2x+15 C. 175 D If m ABD 40 and m ABC 110, find m DBC. A. 150 B. 130 C. 70 D. 80 A B D C 13. Find m RSU if ST bisects RSU, m 1 4x 12 and m 2 2x 6. R A. 48 B T C. 9 D. 24 S U 14. Choose the converse of If 1 2, then m 1 = m 2. A. If m 1 = m 2, then 1 2
5 B. If 1 2, then 2 1 C. If m 1 = m 2, then m 2 = m 1. D. None of these 15. Identify the if-then form of the following: All cars have four wheels. a. If a vehicle has four wheels, then it is a car. b. If a vehicle is a car, then it has four wheels. c. If a vehicle is not a car, then it does not have four wheels. d. None of these 16. The transitive property of equality states If a = b and b = c, then. A. b = a B. a = c C. c = b D. b = b 17. P and Q form a linear pair and m P 62. Find m Q. A. 62 B. 28 C. 118 D Given l m and m 2 = 72, find m 3. ( for 21-23, the rectangle represent parallel lines) A. 108 B. 72 C. 18 D l 19. Given l m, m 1= 9x +5 and m 2 = x + 37, find the value of x. A. 32 B. 4 C. 41 D m
6 20. Given m 4 5x 2 and m 5 = 3x + 28, find the value of x so that l m. A. 26 B. 13 C. 67 D The measures of two angles of a triangle are 38 and 47. What is the measure of the third angle? A. 85 B. 95 C. 133 D If IGH KLJ, then H is congruent to A. J B. I C. K D. L 25. Find the value of x. 26. Find the value of x when a b.
7 27. Solve for x in the diagram. 28. In the diagram, WX YZ. Find the length of XZ. 29. Find the midpoint and distance of a segment with endpoints A(-8, 5) and B(-2, 7). 30. AB bisects CAD. Find the value of x. 31. MQ= 30, MN = 5, MN=NO, and OP=PQ. Find the length of OQ.
8 Find QR in the following problems. 1. If RS = 44.6 and SQ = 68.4, find QR. 2. If RS = 33.5 and RQ = 80, find SQ. If U is between T and B, find the value of x and the measure of TU. (Hint: Draw a picture for each problem with the given information and then write the equation to solve. 22. TU = 2x, UB = 3x + 1, 23. TU = 4x-1, UB = 2x -1, 24. TU = 1-x, UB = 4x+17, TB = 21 TB = 5x TB = -3x Algebraic Proofs: Write a two column proof for the following: Given: Given: 2(2x+3) - 2 = 3(x-1) Prove: x = -7
9 Given: Given: 1/2(2x-4) + 3 = 1/3(3x-9) Prove: x = 4 1. Angle Bisector a. A ray that cuts any angle into two congruent halves b. A ray that cuts any line into two congruent halves c. A ray that cuts any object into two congruent halves d. A ray that cuts any segment into two congruent halves 2. Complementary angles a. Angles whose sum is 180 degrees b. Angles whose sum is 90 degrees c. Angles whose sum is 100 degrees d. Angles whose sum is 0 degrees 3. Supplementary angles a. Angles whose sum is 90 degrees b. Angles whose sum is 0 degrees c. Angles whose sum is 180 degrees d. Angles whose sum is 100 degrees 4. Vertical angles a. Two pairs of congruent angles that are formed when two line intersect b. Four congruent angles that are formed when two line intersect c. One pair of congruent angles that are formed when two line intersect d. Exist only in linear pairs 5. Ruler Postulate: a. Given any two points on a line, the distance cannot be measured b. Given any two points on a line, the distance can be measured c. Given any two points on a line, the distance is imaginary d. Given any two points on a line, there is not distance between them 6. A=B and B=C, then A=C a. Substitution
10 b. Segment addition c. Transitive d. Reflexive 7. If segment AB = 10m and BC = 5m, then segment AC = 15m a. Substitution b. Segment addition c. Transitive d. Reflexive 8. If angle A = 15 and angle B = 75, then their measure is: a. Supplementary b. Perpendicular c. Parallel d. Complementary 9. If a = b, then b = a a. Transitive b. Substitution c. Reflexive d. Symmetric Define the following: 1. Definition of Congruence 2. Perpendicular lines 3. Segment Addition Postulate 4. Angle addition Postulate 5. Protractor postulate
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