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Geometry Name ____________________________________ Unit 3 Celebration of Knowledge Decide whether each statement must be true or false. Use the figure for Exercises 4–8. ______ 1. Two coplanar lines are always parallel. ______ 2. Any two noncoplanar lines are skew. ______ 3. The sum of the interior angles of a polygon is always 360°. ______ 4. 15 and 3 are same-side interior angles. ______ 5. 9 and 15 are alternate interior angles. and 14 are corresponding angles. ______ 6. ______ 7. If 1 5 , then . ______ 8. If 10 and 7 are supplementary, then Find and 9. . . State the theorems or postulates that justify your answers. 10. 11. Use the given information to determine which lines must be parallel. State the theorem or postulate that justifies your answer. If there are no such lines, write none. 12. 3 8 13. 2 10 14. 4 5 180 15. 7 10 16. 3 4 180 17. 6 9 Find the values of the variables. 18. 21. 19. 20. 22. 23. What is the measure of an interior angle of a regular 24-gon? 24. What is the measure of an exterior angle of a regular 15-gon? Determine whether the following pairs of lines are parallel, perpendicular, or neither. JUSTIFY. 1 25. 26. y x 7 27. 28. y 4 3 x3 6x 2 y 8 Write the equation of each line described in point-slope form. 29. The line has slope of 6 and contains . 30. The line passes through (-2, 4) and (6,8). 31. The line is perpendicular to y 3 x 6 and contains (-4, 9). 32. Use intercepts to graph the following. 3 x 7 y 21 33. Use the slope and y-intercept to graph the following. 5 y x4 3 34. Prove the following theorem: The acute angles of a right triangle are complementary. Given: ΔABC with right angle C Prove : A and B are complementary Statements Reasons 1. ABC with right angle C 1. Given 2. mC 90 2. _____________________________ 3. _____________________________ 3. Triangle Angle-Sum Theorem 4. mA mB 90 180 4. _____________________________ 5. mA mB 90 5. _____________________________ 6. A and B are complementary 6. _____________________________ BONUS: Find the value of w in the following figure.