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Transcript
Name Class Date Topic 3 Test Review Use the figure for Exercises 1-8. For Exercises 1–8, suppose a || b and c || d. 1. 2 and 10 are what kind of angles? 2. 3 and what angle are alternate interior angles? 3. 9 and 8 are what kind of angles? 4. Which angle could you show is congruent to 11 to prove a || b? 5. What relationship between 6 and 11 to shows c || d? 6. If m6 50 , then find m11 . 7. If m2 70 , then find m6 . 8. If m1 130 , then find m5 . 9. Suppose a line intersecting two lines a and b forms a 35° angle with each line. What are the possible relationships between lines a and b? Explain. (Hint: Draw a picture.) 10. Find the value of the variables in the triangle at the right. 11. Explain how perpendicular lines can be used to construct a line parallel to a given line. 12. Find the slope of the line passing through (–6, –2) and (–3, –6). 13. Find the equation of the line with a slope 6 and y-intercept 4. 14. Find the equation of the line passing through (10, 2) and (2, –2). Name Class Date Topic 3 Test (continued) 15. A triangle has 1 and 2 as remote interior angles with respect to exterior angle 3 . Given that m1 50 and m2 70 , Alicia reasoned that m3 must be 60. Explain Alicia’s error. Determine whether the following pairs of lines are parallel, perpendicular, or neither. 16. y = 2x + 1 2x + y = 7 17. y = 1 3 18. y = –4x + 1 x+4 4x + y = –3 3x + y = 2 19. What is the equation of the line parallel to y = x – 1 that contains the point (1, 2)? 20. What is the equation of the line perpendicular to y = 1 2 x + 1 that contains the point (–2, 1)? Classify each set of angle measures as the angle measures of a triangle in Euclidean geometry, a triangle in spherical geometry, or neither. 21. 28, 46, 75 22. 25, 45, 130 23. 22, 55, 103 24. Water Street intersects 25th Street and 28th Street at right angles. Highway 47 is parallel to 28th Street. How are 25th Street and Highway 47 related? Explain. For Exercises 25-26, determine whether each of the following properties of Euclidean geometry is true in spherical geometry. 25. A line segment is the shortest distance between two points. 26. Through a point not on a line, there is one and only one line parallel to the given line. 27. Draw a line m and a point Q not on the line. Construct the line through Q parallel to line m.