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GEOMETRY WKST 3.1-3.2 CHAPTER 3 SECTION 1 - 2 NAME_______________________________HOUR_____ DATE_____/_____/_____ Score: For exercises 1 – 4, refer to the figure at the right. 1. Name all planes that are parallel to plane DEH.______________________________ 2. Name all segments that are parallel to AB .__________________________________ 3. Name all segments that intersect GH . _____________________________________ 4. Name all segments that are skew to CD . ___________________________________ Identify the sets of lines to which each given line is a transversal. 5. r 6. s 7. w ______________ ______________ _______________ Identify each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. 8. 2 and 8 9. 3 and 6 ___________________________ ___________________________ 10. 1 and 9 11. 3 and 9 ___________________________ ___________________________ 12. 6 and 12 13. 7 and 11 ___________________________ ___________________________ Name the transversal that forms each pair of angles. Then identify the special name for the angle pair. 14. 4 and 10 15. 2 and 12 ___________________________ ___________________________ 16. 7 and 3 17. 13 and 10 ___________________________ ___________________________ 18. 8 and 14 19. 6 and 14 ___________________________ ___________________________ In the figure, m2 70 . Find the measure of each angle. 20. 3 21. 5 22. 8 ______________ ______________ _______________ 23. 1 24. 4 25. 6 ______________ ______________ _______________ In the figure, m7 100 . Find the measure of each angle. 26. 9 27. 6 28. 8 ______________ ______________ _______________ 29. 2 30. 5 31. 11 ______________ ______________ _______________ In the figure, m3 75 and m10 115 . Find the measure of each angle. 32. 2 33. 5 34. 7 ______________ ______________ _______________ 35. 15 36. 14 37. 9 ______________ ______________ _______________ Find x and y in each figure. 38. x = ________ y = ________ 39. x = ________ y = ________ Find m1 in each figure. 40. m1 = ________ 41. m1 = ________ GEOMETRY PF WKST 3.3-3.5 CHAPTER 3 REVIEW SECTIONS 3-5 NAME__________________________________HR_____ DATE_____/_____/_____ Score: Determine the slope of the line that contains the given points. 1. S(-1, 2), W(0, 4) 2. J(-5, -2) K(5, -4) Determine whether AB and MN are parallel, perpendicular, or neither. 3. A(0, 3) B(5, -7) M(-6, 7) N (-2, -1) 4. A(-4, -8) B(4, -6) M(-3, 5) N(-1, -3) Graph the line that satisfies each condition. 5. (2, -3) m 4 5 6. passes through (-3, -1), 7. passes through (3, 0), parallel to a line whose slope is -1 perpendicular to a line whose 3 slope is 2 Write an equation in slope-intercept form for the given information. 8. m 3 , (4, 6) 2 11. (2, -4) (5, 8) 10. x –intercept: -6, y-intercept: 2 9. m = 3, (2, -3) 12. (3, 5), parallel to m 1 3 13. (-2, 7), perpendicular to m 2 3 Given the following information, determine which lines, if any, are parallel. State a reason to justify your answer. 14. 3 7 15. 9 11 16. 2 16 17. m5 m12 180 Find x so that l m . 18. 19. 20. Fill in the reasons in the following proof. 21. Determine whether each pair of lines is parallel. Explain your answer. 22. 23. GEOMETRY PF Review WKST 3.1-3.5 CHAPTER 3 STUDY GUIDE NAME__________________________________HR_____ DATE_____/_____/_____ Refer to the diagram at the right. State the transversal that forms each pair of angles. Then identify the special angle relationship, if one exists. If the angles do not form a special angle relationship, write NONE. Score: l B m 4 3 1. 1 & 5 trans:________ 2. 1 & 2 trans:_______ 5 2 _______________________ __________________________ A 3. 4 & 10 trans:_______ 4. 2 & 7 trans:_______ 1 6 11 7 C 8 10 9 _______________________ __________________________ In the figure below, a ║ b , CB║DF, DE bisects CDF and m4 = 110. Find the measure of each angle. Justify your answer with a postulate or theorem. 5. m5 = ________ E D B 6. m13 = ________ 4 3 C 7. m12 = ________ F 10 9 8 5 7 6 a b 1 2 11 12 14 15 13 D 8. m15 = ________ 9. State which lines, if any, are parallel. State the reason that justifies your answer. ______________________________ c 68 66 112 d a b Reason:_____________________________________________________ __________________________________________________ Find the value of x so that l║m. Then justify all work with the appropriate reasoning. 10. m l work: b/c: work: b/c: (3x+10) (6x-20) 11. m (2x-16) l 62 12. work: (3x-20) m l b/c: (2x) 13. Using the points A (-2, 5) and B (4, 9) answer each of the following. a. Find the slope of the line passing through the points A and B. b. State the slope of a line parallel to AB and explain why. c. State the slope of a line perpendicular to AB and explain why. work: Slope = ________ Explanation: Slope = ________ Slope = _________ Explanation: 14. Write an equation in slope-intercept form of 15. Write an equation in slope-intercept form of 3 the line that has m= and contains (6, -1) 4 Equation:_______________________ Equation:____________________________ 16. Write an equation in slope-intercept form for the line that contains point (3, 5) and is parallel to y the line that contains (2, -4) and (5, 8). 1 x 3. 2 17. Write an equation in slope-intercept form for the line that contains (-2, 7) and is perpendicular y 3x 2 Equation:_______________________ Equation:_________________________ 18. Find the measure of each angle: m8 30, m9 110 m1 ________ m2 ________ m3 ________ m4 ________ m5 ________ m6 ________ m7 ________ m10 ________ m11 ________ m12 ________ m13 ________ m14 ________ Write whether each statement is true or false. If false, replace the underlined word with the word that would make the sentence true. _____20. 4 & 5 are alternate exterior angles. _______________________ _____21. The ratio of the rise to the run of a line is called slope. _____________________ _____22. If two lines do not intersect and are noncoplanar then they are parallel. _____________________ _____23. Exterior angles are located between the lines cut by a transversal. _____________________ _____24. The equation y = 5x -3 is in point-slope form. _____________________ Complete a proof for each. 26. Given: 3 6 25. Given: a b Prove: 3 6 4 5 Prove: a b (Do NOT use: If lines are ║ , then alt int s ) Statements (Do NOT use: If alt int s then lines are ║.) Reasons Statements Reasons t 1 Fill in the reasons on the following proof. 27. Given: ab 2 ta Prove: t b Statements a b Reasons 1. a b, t a 1.______________________________________________ 2. 1 is a right angle 2.______________________________________________ 3. m1 90 3.______________________________________________ 4. 1 2 4.______________________________________________ 5. m1 m2 5.______________________________________________ 6. m2 90 6.______________________________________________ 7. 2 is a right angle 7.______________________________________________ 8. t b 8.______________________________________________