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Geometry CST Std 2-3-22 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Drawings are very helpful when writing a proof. Which of the following can be assumed from a a. . b. M bisects diagram? noncollinear with A and B. d. a. right angles b. supplemental angles c. parallel lines d. congruent segments . c. M is . 3. Another name for a proof using contradiction is: a. indirect proof b. inductive reasoning 2. Segment has a midpoint, M. What conclusion c. paragraph proof d. two-column proof can you draw? 4. Sean is trying to prove the theorem below using proof by contradiction. Using the diagram below, he assumes that is not congruent to . Which theorem will Sean use to reach a contradiction? Theorem: Vertical angles are congruent. 2 3 1 4 a. All right angles are congruent. b. If two angles are supplementary to the same angle, then they are congruent. c. The sum of supplementary angles sum is 180º. d. If two angles are supplementary and congruent, then they are right angles. 5. Use the proof to answer the question below. measure 90º. c. Substitution d. Supplementary angles are congruent. Given: are right angles. Prove: 6. When using proof by contradiction, what is the first step? Statements Reason a. Assume what you are trying to prove is true. s b. Assume what you are trying to prove is false. 1. are right angles. 1. Given c. Use the given information to complete a proof. 2. m = 90º 2. d. Assume no given statements are true. Definition of right angle. 3. m = 90º 3. 7. Which of the following is not a type of proof? Definition of right angle. 4. 4. ? a. Paragraph b. Two-column c. Indirect d. Conditional What reason can be used to prove the angles are congruent? 8. Use the proof to answer the question below. a. Definition of right angle. b. All right angles Given: Prove: 12. Point A has coordinates of (–3, 2). What conclusion can you draw? D F 1 A 2 a. Point A is in Quadrant II. b. Point A is on the xaxis. c. Point A is in Quadrant III. d. Point A is not in a quadrant. 3 B C 13. What is the converse of the statement: “If two angles are vertical angles, then they are congruent.” Statements Reasons 1. 2. Addition Property of Equality 3. Addition Property of Equality 4. Substitution 5. Reflexive Property 6. 1. Given 2. 3. 4. 14. If a conditional statement is true, which of the following statements must also be true? 5. 6. ? a. inverse b. converse c. contrapositive d. biconditional a. Substitution Property of Equality b. CPCTC c. Subtraction Property of Equality d. Addition Property of Equality 15. “If two angles are right angles, then they are congruent.” 9. The Reflexive Property can be used to prove which of these statements? a. d. b. are right angles. a. Vertical angles are congruent. b. If two angles are congruent, then they are vertical angles. c. If two angles are not vertical angles, then they are congruent. d. If two angles are not vertical angles, then they are not congruent. The validity of the converse of this statement is: a. true b. false c. cannot be determined d. There is no converse. c. 16. Which figure can serve as a counterexample to the conjecture below. 10. Which shows an example of the Symmetric Property? Conjecture: Every triangle has two congruent sides. a. If then then then , then . c. If . d. If . . b. If , and , and 11. “Two planes intersect in exactly one line.” Which of the following would best serve as a counterexample to the conjecture above? a. intersecting planes b. perpendicular planes c. parallel planes d. coplanar lines , , , a. isosceles triangle b. equilateral triangle c. scalene triangle d. isosceles right triangle 17. What is the inverse of the statement: “If two angles are right angles, then the angles are supplementary.” a. If two angles are not right angles, then they are not supplementary. b. If two angles are supplementary, then they are right angles. c. If two angles are right angles, then they are not supplementary. d. If two angles are not supplementary, then they are not right angles. 18. Which of the following is an example of a true conditional statement? a. If two triangle are right triangles, then the triangles are congruent. b. If a figure has 4 sides, then it is a parallelogram. c. If an angle is obtuse, then it has a measurement less than 90º. d. If a figure is a square, then it is a rectangle. 23. What is the reflection of the point (5, 8) over the line y = x? a. (–5, –8) b. (–8, –5) c. (8, 5) d. (5, 5) 24. If triangle XYZ is rotated 90º closewise about the origin, what are the coordinates of ? y 19. Sandy’s friend Oliver told her, “If I am wet, then it is raining outside.” Sandy does not believe his statement is always true. Which of the following statements could she not use as a counterexample? a. Oliver forgot his umbrella and got caught in the rain. b. Oliver just finished swimming. c. Oliver just took a shower. d. Oliver was water skiing. 5 4 Z 3 X 2 1 –5 –4 –3 –2 –1 –1 1 –2 20. “If three points are collinear, then they form a triangle.” 2 3 4 5 x Y –3 –4 –5 Which of the following is the contrapositive of the conjecture? a. (2, –3) b. (–2, 3) c. (–2, –3) d. (–3, –2) a. If three points do not form a triangle, then they are noncollinear. b. If three points are noncollinear, then they do not form a triangle. c. If three points do not form a triangle, then they are not noncollinear. d. If three points form a triangle, then they are collinear. 21. The vertices of are X(5, 4), Y(1, –3), and Z(– 2, 2). is translated 2 units down and 2 units to the right. What are the new coordinates for the vertices of the triangle? 25. Regular pentagon FGHJK is shown below. What point represents a 144º clockwise rotation of point G about point Y? F K G a. X(7, 2), Y(3, –5), Z(0, 0) b. X(7, 6), Y(3, –1), Z(– 4, 4) c. X(3, 2), Y(3, –5), Z(0, 4) d. X(3, 2), Y(3, – 1), Z(–4, 4) 22. Sean has a piece of paper with a word written on it. He cannot read the word unless he holds it up to a mirror and reads the word in the mirror. Which of the following describes the transformation that allows Sean to read the word? a. reflection b. rotation c. tessellation d. translation Y J a. F b. H c. J d. K H 26. The diagram below shows a translation of the solid image to the dotted image. Which rule describes the translation? y 9 8 7 6 5 4 3 2 1 –7 –6 –5 –4 –3 –2 –1 –1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 x –2 –3 –4 a. (x + 3, y + 3) b. (x + 7, y + 3) c. (x – 7, y – 3) d. (x – 3, y – 7) 27. Alli needs to rotate a figure 180º about the origin. The coordinates of one of the points is (x, y). Which of the following represents the coordinates of the point after the rotation? a. (y, x) b. (–x, –y) c. (–x, y) d. (x, –y) 28. Which of the following figures does not have a line of symmetry? a. b. c. d. 29. Which of the following describes the transformation shown? a. translation b. rotation c. reflection d. symmetry 30. Maureen hung a picture on the wall. It was 4 feet from the floor. She moved the picture right 1 foot and up 2 feet. How high is the picture from the floor? a. 4 ft b. 5 ft c. 6 ft d. 7 ft