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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 the line that has m= 3 and contains (6, -1) 4 Equation:_______________________ the line that contains (2, -4) and (5, 8). Equation:____________________________ 16. Write an equation in slope-intercept form for the line that contains point (3, 5) and is parallel to y 15. Write an equation in slope-intercept form of 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 Prove: a b 4 5 (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 ta Prove: t b Statements 2 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.______________________________________________