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Geometry Unit 3 Corrective 1 Revised Summer 08 Show all work on a separate sheet of work paper. Remember to follow the criteria for credit. Competency 1: Lines and Angles Terminology Competency 2: Angles Associated with Transversals For questions 1 and 2, refer to the following diagram. For questions 6 and 7, use the following diagram. State the measure of the angle and justify your answer. a b K G H J D C 1 2 c E F 126˚ B d A 1. Name two lines that are skew to 2. Name two lines that are perpendicular to . Given: a || b and c || d . 6. For questions 3 – 5, classify each pair of angles as alternate interior angles, consecutive (same side) interior angles, alternate exterior angles, corresponding angles, or vertical angles. Use the following diagram for all 3 questions. Statement: m1 Reason: Angle 1 is ____ to 126° 7. Statement: m2 Reason: Angle 2 is ____ to angle 1. For questions 8 - 10, use the following diagram. If lines are parallel, state the theorem you need to use to justify your answer. 3. 2 and 4 4. 4 and 5 5. 6 and 7 8. Page 1 of 4 © Mastery Mathematics If 6 7 , which lines, if any, must be parallel? Geometry Unit 3 Corrective 1 If 6 3 , which lines, if any, must be parallel? 9. 15. Given that q || r and s t, solve for x. s If 8 and 11 are supplementary, which lines, if any, must be parallel? 10. Revised Summer 08 (4x)° q Competency 3: Solve Problems Applying Angle Properties t (6x - 40)° 11. Given AB || CD, solve for x. D (4x - 40)° r C Competency 4: Slope/ Equations of Lines 16. Find the slope of the line passing through ( -5, -6 ) and ( -5, 4 ). 17. Find the slope of the line passing through ( -2, -3 ) and ( -6, 1 ). 18. Given the coordinates of points A, B, C, and D, use the slope of lines to determine if AB and CD are parallel, perpendicular, or neither. A ( -1, 4 ) B ( 2, 8 ) C ( -4, 1 ) D ( 0, -2 ) 19. Write an equation of a line that has a yintercept of 0 and is parallel to y = x + 4. 20. The relationship cannot be determined from the given information. (2x - 20)° A 12. B Given MP || NQ, solve for x. L M N (3x + 7)° P (7x - 5)° Q 13. Given that a || b, solve for x. t a perpendicular to y (3x + 25)° Write an equation of a line that has a yintercept of -6 and is Competency 5: Two Column Proofs b (5x - 15)° 14. Given that k || m, solve for x. n k 2 x 5. 3 (x + 80)° m Page 2 of 4 (3x - 10)° © Mastery Mathematics Geometry Unit 3 Corrective 1 Use the diagram to complete the proof. A B C D t E F H G s Revised Summer 08 c. If Marie does not have soccer practice, then it is not Tuesday. d. Mare has soccer practice if and only if it is Tuesday. e. None of the above. 27. Two angles, 7 and 8 , are both supplementary to 9 . If m7 =61°, what is m8 ? a. 29° b. 61° c. 90° d. 119° e. 180° GIVEN: s//t and mA = 120° PROVE: mH = 60° STATEMENT REASON s//t GIVEN 21.______________ GIVEN 22. m D 23. Angle D is _____ to angle A ( _____ Theorem) = ___° m E = 120° 24. Angle E is _____ to angle D (_____ Theorem) m H = 60° 25. Angle H is ______to angle E (Definition of _____ Angles) 28. Two angles PQR and RQS form a linear pair. If mPQR =73°, what is mRQS ? a. 73° b. 107° c. 17° d. 90° e. 180° 29. Let p be “there is lightning” and let q be “we cannot go hiking.” What is ~p ~q? a. If there is lightning, then we cannot go hiking. b. If we can go hiking, then there is no lightning. c. If we cannot go hiking, then there is lightning. d. If there is no lightning, then we can go hiking. e. None of the above. 30. Consider the two quantities that are described below. Column A Competency 6: Distributive Practice: 26. What is the inverse of “If it is Tuesday, then Marie has soccer practice”? a. If it is not Tuesday, then Marie does not have soccer practice. b. If Marie has soccer practice, then it is Tuesday. Page 3 of 4 © Mastery Mathematics The sum of the measure of two complementary angles. Column B The sum of the measure of two supplementary angles. Choose the statement that is true. a. The quantity in Column A is greater. Geometry Unit 3 Corrective 1 b. The quantity in Column B is greater. c. The two quantities are equal. Page 4 of 4 © Mastery Mathematics Revised Summer 08