Geometry First Semester Exam Review

Transcription

1 Geometry First Semester Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Name three points that are collinear. a. points T, Q, and R c. points S, Q, and R b. points T, Q, and S d. points T, S, and R 2. is represented by which sketch? a. c. b. d. 3. If RS = 31.4 and QS = 65.2, find QR. a b c d Find the midpoint of the segment with endpoints ( 9, 8) and ( 2, 9). a. ( 7 2, 1 2 ) c. ( 11, 17) b. ( 11 2, 17 2 ) d. ( 17, 11) 5. The nonshared sides of two adjacent angles form a pair of opposite rays. The angles are. a. acute b. complementary 1

2 c. a linear pair d. vertical angles 6. Name a polygon with 6 sides. a. pentagon b. octagon c. quadrilateral d. hexagon 7. Find the circumference of the circle. Use = a in. b in. c in. d in. 8. If the pattern indicated below is continued, what would be the total number of cubes in the 7th stage of the pattern? a. 64 b. 140 c. 8 d Rewrite the statement in if-then form. Every triangle has three sides. a. If a figure has three sides, then it is a triangle. b. If a figure is a triangle, then it has three sides. c. A figure is a triangle if and only if it has three sides. d. A figure has three sides if and only if it is a triangle. Choose the phrase that completes the following statement as stated by the Point, Line, and Plane Postulates: 10. One plane passes through three noncollinear points. a. always b. never c. sometimes d. Point, Line, and Plane Postulates do not address this topic directly. 11. A line contains at least two points. a. always b. never c. sometimes d. Point, Line, and Plane Postulates do not address this topic directly. 12. Identify the property of congruence. 2

3 a. Symmetric Property of Congruence c. Substitution Property b. Transitive Property of Congruence d. Reflexive Property of Congruence 13. In the figure shown,. Which of the following statements is false? A D E B C a. b. c. d. 14. Solve for x. a. 3 c. 1 b. 6 d Two lines that are not coplanar and do not intersect are called. a. Parallel c. perpendicular b. oblique d. skew lines 16. Use the figure to find the measure of a. c. b. d. 17. Refer to the figure. Which theorem guarantees l and m are parallel? 3

4 a. Alternate Interior Angles Converse b. Consecutive Interior Angles Converse c. Corresponding Angles Converse d. Alternate Exterior Angles Converse 18. Find the slope of the line passing through the points A( 7, 4) and B(0, 9). a. 13 c b. 7 d Which graph shows the line that passes through and is parallel to a line with a slope of 2? a. y 10 c. 10 y x x b. 10 y d. 10 y x x Classify GHI. 4

5 a. Equilateral b. Scalene c. none of these d. Isosceles 21. Name an obtuse triangle. a. none of these b. c. d. 22. Find the value of x: a. 85 b. 28 c. 123 d Find the value of x. 5

6 a. 297 b. 66 c. 117 d Find the value of x. a. b. c. d. 25. The two triangle-shaped gardens are congruent. Find the missing side lengths and angle measures. a. q = 4 ft; r = 24 ; s = 66 ; t = 90 ; u = 4 ft b. q = 4 ft; r = 24 ; s = 90 ; t = 66 ; u = 9.8 ft c. q = 4 ft; r = 24 ; s = 90 ; t = 66 ; u = 4 ft d. q = 9 ft; r = 24 ; s = 90 ; t = 66 ; u = 9.8 ft 26. If which statement is NOT true? a. c. b. d. Explain how you know the triangles are congruent. Then write an equation and solve for x. 6

7 27. a. Side-Angle-Side; c. Side-Angle-Side; b. Side-Side-Side; d. Side-Side-Side; 28. Determine which triangle is congruent to the given triangle. a. none of these c. b. d. 29. Refer to the figure below. Which of the following statements is true? 7

8 I J L H K a. by SAS c. by SSS b. There are no congruent triangles. d. by SSS 30. Refer to the figure shown. Which of the following statements is true? a. c. b. d. 31. Given: and. What other piece of information is needed to show by ASA Congruence Postulate? a. b. c. d. = 32.. Name the theorem or postulate that justifies the congruence. a. HL b. AAS c. ASA d. SAS Numeric Response 8

9 1. GRIDDED RESPONSE Grid the correct answer on a separate gridding sheet. Lines a and b in the figure below are parallel. What is the measure of in degrees? Completion Complete each statement. Fill in the correct word(s) to make the statement true. 1. A diagram using arrows to show how to get from one statement to the next is called a. Short Answer 1. Name a ray from Q through P. 2. If AB = 19 and AC = 32, find the length of 3. If AB = 11 and AC = 25, find BC. 4. Find the distance between the points ( 4, 5) and ( 8, 2). 5. If and, then what is the measure of? 9

10 6. m JHI = ( ) and m GHI = ( ) and m JHG = 65. Find m JHI and m GHI. 7. Classify the angle as right, acute, or obtuse. Complete the conditional statement to make a true statement. 8. If and are supplementary and, then. 9. Solve for x: 10

11 ( 3x + 58 ) (4x + 101) 10. Find the perimeter and area of a rectangle with length 150 ft and width 15 ft. 11. Find the area: 12. Provide the reasons for each statement in the proof. Given: Prove: A B C D E 13. Is the statement true or false? Explain your reasoning. Intersecting lines are always parallel lines. True or False, (if False explain why): 14. If two parallel lines are intersected by a transversal, then alternate interior angles are congruent. 11

12 Which lines, if any, can be proved parallel given the following diagram? For each conclusion, provide the justification. 15. a b c d Use the given angle measures to decide whether lines a and b are parallel. Write Yes or No. 16., 17. Find the slope of the line passing through the points A(4, 4) and B( 3, 3). 18. Find the slope of the line. 10 y 10 x 10 12

13 19. What is the slope of a line parallel to the line? 20. Write an equation for the line passing through the point that has a slope of True or False: If two lines are perpendicular to the same transversal, then they are parallel. 22. Suppose,. True or false: 23. The two triangle-shaped gardens are congruent. Find the missing side lengths and angle measures. 9 f c a 409 ft 20 ft d e 3 ft b Would HL, ASA, SAS, AAS, or SSS be used to justify that the pair of triangles is congruent? 24. Other 1. Determine if the figure below is a polygon. If it is not a polygon, explain why. 2. Determine if the figure below is a regular polygon. If it is not a regular polygon, explain why. 13

14 3. Give one counterexample that shows the conjecture is false. In a coordinate plane, if the x-coordinate of a point is positive, then the point is in the first quadrant. 4. Identify the hypothesis and conclusion of the statement. If today is Tuesday, then yesterday was Monday. 5. Given that: i. Tawana bought a new computer. ii. All computers depreciate in value. What conclusion can be logically deduced? 6. Write the conclusion to be drawn from the two pieces of given information: 7. Name the property which justifies the following conclusion: Given: Conclusion: 8. Name the property which justifies the following conclusion: Given: Conclusion: 14

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