Competency 1: Angles and Angle Bisectors 1. What is the classification of an angle that has a measure of less than 90 o? 4. Given the diagram below where BD is an angle bisector. A D 2. Given the following diagram: B C W M If the m ABC = 14 o and m DBC= (3x+1) o, then what is the value of x? X Y If WXY is a right angle and m WXM = 25, then what is the m MXY? 3. Given the following diagram: If T Q R S QRS is a straight angle and m QRT = 26, then what is the m TRS? 5. Given the diagram below and BD is an angle bisector. B A D C If the m ABD = (5x + 7) o and m DBC= (21 2x) o, then what is the value of x? Revised 8/26/2012 page 1 of 6 Printed 8/30/2012
Competency 2: Angle Pair Relationships 9. Given the following diagram: 2 3 4 (7x + 4) (2x - 13) 1 6 What is the value of x? 5 9 8 7 6a. Using the above diagrams, identify a pair of complementary angles. 6b. Using the above diagrams, identify a pair of supplementary angles. 7. Using the above diagrams, identify a pair of vertical angles. 10. Given the following diagram: 8. Given the following diagram: (2x - 30) y x (2x + 14) (3x + 6) What is the value of x and y? What is the value of x? Revised 8/26/2012 page 2 of 6 Printed 8/30/2012
Competency 3: Conditional Statements 11. Given the conditional statement: If an angle is an obtuse angle, then the measure of the angle is greater than 90 o. a) Is the given statement true or false? 13. Given the following conditional statement: If the product of two integers is positive, then the two integers must be negative. a) Is the given statement true or false? b) What is the inverse? b) Write the contrapositive. c) Classify the inverse as true or false. If false, provide a counterexample. c) Classify the contrapositive as true or false. 14. Given the following conditional statement: If it is first hour, then I am in math class. What is a counterexample that proves the conditional statement false? 12. Given the conditional statement: If two angles are supplementary, then the sum of the two angle measures is 180. a) Is the given statement true or false? b) What is the converse? 15. Given the following conditional statement: If the sum of two numbers is positive, then both numbers must be positive. What is a counterexample that proves the conditional statement is false? c) Classify the converse as true or false. Revised 8/26/2012 page 3 of 6 Printed 8/30/2012
Competency 4: Deductive Reasoning 16. State whether the following argument is valid or invalid. If it is invalid, briefly explain why. If a figure is a triangle, then it is a polygon. I drew a figure that is a polygon. Therefore, the figure that I drew is a triangle. 19. The statements below are out of order. 1. If a figure is a square, then it is a rhombus. 2. If a figure is a parallelogram, then it is a quadrilateral. 3. If a figure is a quadrilateral, then it is a polygon. 4. If a figure is a rhombus, then it is a parallelogram. Which of the following lists the statements in the correct logical order? 17. State whether the following argument is valid or invalid. If it is invalid, briefly explain why. If today is Saturday, then I go to work. Today is Saturday. Therefore, I go to work. a. 2, 4, 3, 1 b. 1, 4, 2, 3 c. 3, 2, 1, 4 d. 4, 2, 3, 1 Competency 5: Distributed Practice 18. If the following two premises (statements) are true, what conclusion can you reach? A scalene triangle has 3 sides that are different lengths. ABC has 2 sides that are the same length. Conclusion: 20. Given the following sequence: a 0 =2, a 1 =4, a 2 =8, a 3 =16, a 4 =32 Which formula generates the correct output? a. a n = 2n + 5 b. a n = (n 1) 2 c. a n = 5n 3 (n + 1) d. a n = 2 Revised 8/26/2012 page 4 of 6 Printed 8/30/2012
21. Given the following number line where YZ = 3a 8, XY = 5a + 3, and XZ = 31 4a: X Y Z What is the value of XY? 23. One endpoint of AB is located at 4,6. If the midpoint of AB is ( ) located at ( 8, 3), what are the coordinates of the other endpoint? a. ( 4, 3) b. ( 2,1.5 ) c. ( 20, 12) d. ( 12,3 ) 22. The algorithm below is a step-by-step calculation. I. Subtract the first y-coordinate from the second y-coordinate. II. Subtract the first x-coordinate from the second x-coordinate. III. Express your answer as a ratio of the answer from Step I over the answer from Step II. Which calculation does the algorithm best represent? a. Calculating the slope of a line. b. Calculating the y-intercept of a graph. c. Calculating the length of a line segment. d. Calculating the midpoint of a line segment. Revised 8/26/2012 page 5 of 6 Printed 8/30/2012
Answers: 1. acute 2. m MXY = 65 3. m TRS = 154 4. x = 2 5. x = 2 6a. 3 and 4 6b. Possible answers: 1 and 2 6 and 7 7 and 8 8 and 9 9 and 6 7. Possible answers: 7 and 9 6 and 8 8. x = 14 9. x = 21 10. x = 30; y = 150 11a. True 11b. If the measure of an angles is not greater than 90 o, then the angles is not an obtuse angle. 13a. False, the two integers could both be positive and have a positive product. 13b.. If the product of two integers is not positive, then the two integers must not be negative. 13c. True 14. Answers will vary. I could have math class fifth hour. 15. Answers will vary. (pos) + (neg) = (pos) (5) + ( 3) = 2 (pos) + (neg) = (pos) (5) + ( 3) = 2 16. Invalid, explanations will vary Since the figure is a polygon, it could be a square. 17. Valid 18. ABC is not a scalene triangle 19. B 20. D 21. XY = 18 (a = 3) 22. A 23. C 11c. True 12a. True 12b. If the sum of two angles measures is 180, then the two angles are supplementary. 12c. True Revised 8/26/2012 page 6 of 6 Printed 8/30/2012