Assignment. Visiting Washington, D.C. Transversals and Parallel Lines

Transcription

1 Assignment Assignment for Lesson.1 Name Date Visiting Washington, D.C. Transversals and Parallel Lines Do not use a protractor in this assignment. Rely only on the measurements given in each problem. 1. Find the measures of the missing angles in the figure below. List the angle measures and the reasons you used for finding them in the table Measure Reason or Justification Line n is perpendicular to line m. Line is perpendicular to line m. Is it possible for line n and line to be skew? Explain. Chapter Assignments 61

2 3. Find the measures of the missing angles in the figure below. List the reasons you used for finding them in the table m 11 68º Measure Reason or Justification Using the figure in Question 3, name two pairs of the each type of angle pairs. 4. Same-side interior angles. Same-side exterior angles 6. Corresponding angles 7. Alternate exterior angles 62 Chapter Assignments

3 Assignment Assignment for Lesson.2 Name Date Going Up? Introduction to Proofs In each conditional statement, identify the hypothesis and the conclusion. 1. If you study and do your homework, then you will do well in math. 2. If you fall off your bicycle, then you will get hurt. 3. If pigs can learn how to fly, then your geometry teacher will loan you money. 4. Write your own conditional statement, identify the hypothesis and conclusion.. Fill in the blanks in the two-column proof to show that if 1 2 and 1 and 2 are complementary, then 1 must have a measure of 4. Statement Reason Given 2. 1 and 2 are complementary m 1 m 2 90º Definition of congruence. m 1 m 1 90º. Substitution Combine like terms m 1 90º Simplify. Chapter Assignments 63

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5 Assignment Assignment for Lesson.3 Name Date Working with Iron Parallel Lines and Proofs In the figure below, m 1 63º. Use this information and the figure to prove that m 4 13º. p q 1 m 2 3 n 4 Statement Reason 1. m 1 63º 1. Given Given 3. p is perpendicular to m m 90º 4... When two parallel lines are cut by a transversal, the alternate exterior angles are congruent. 6. m 1 m Congruent angles have the same measure Definition of congruence Congruent angles have the same measure Exterior Angle Theorem Substitution Combine like terms. Chapter Assignments 6

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7 Assignment Assignment for Lesson.4 Name Date Parking Lot Design Parallel and Perpendicular Lines in the Coordinate Plane State whether each pair of lines is parallel, perpendicular, or neither. Explain your answer using a complete sentence. 1. y 4x 18 y 4x 2. y 2x 6 y 1 2 x 9 3. y 6x y 1 6 x 4. 2y 2x 10. y 1 2 x 7x 2 y y 7x 6. y x y x Chapter Assignments 67

8 7. x y 2 8. Write the equations of 3 lines that are parallel to y 2 x Write the equations of 3 lines that are perpendicular to y 4x Write the equation of a line that is perpendicular to y 1 x Write the equation of a line that is perpendicular to the line in your answer to Question Is the line from your answer in Question 11 parallel, perpendicular or neither to the original line in number 10? Explain. 68 Chapter Assignments

9 Assignment Assignment for Lesson. Name Date Building a Henge Exploring Triangles in the Coordinate Plane On the grid below draw a triangle in the circle that is not a right triangle. Label the vertices D, E, and F. y x 9 1. Use the Midpoint Formula to find the midpoints of DE, EF, and FD. Mark these points on your drawing. Label them H, K, and L. 2. Draw HK, KL, and LH. 3. Find the slopes of DF and HK. Chapter Assignments 69

10 4. Find the slopes of DE and LK.. Find the slopes of EF and HL. 6. What do you notice from your answers to Questions 3, 4, and? 7. Are the slopes of the line segments that look parallel exactly equal? Why do you think this might be so? 70 Chapter Assignments

11 Assignment Assignment for Lesson.6 Name Date Building a Roof Truss Angle and Line Segment Bisectors 1. If you bisect an angle that measures 137, what are the measures of the two newly formed angles? Explain how you found your answer. 2. Measure each angle in this triangle and write your results in the figure. Then draw three angle bisectors in the triangle, measure each newly formed angle, and write your results in the figure. 3. Can all angles be bisected? Use a complete sentence to support your reasoning. 4. If you bisect an angel that measures 6, and then bisect each newly formed angle, how many angles do you create? What is the measure of each angle? Chapter Assignments 71

12 . Draw an acute angle on the starter ray in the figure, and draw the angle bisector. Justify your results by measuring the angles with a protractor and recording the measures in the figure. 6. Draw an obtuse angle on the starter ray in the figure and draw the angle bisector. Justify your results by measuring the angles with a protractor and recording the measures. 7. If you bisect a 1 centimeter line segment, what are the measures of the two newly formed segments? Explain how you found your answer. 72 Chapter Assignments

13 Name Date 8. Measure each side of the triangle below and write your results in the figure. Then draw three segment bisectors in the triangle, measure each newly formed segment, and write your results in the figure. 9. Can all line segments be bisected? Use a complete sentence to support your reasoning. 10. If you bisect a 20-centimeter segment and then bisect each newly formed segment, how many segments do you create? What is the measure of each segment? 11. Draw an 8-centimeter segment on the starter ray and bisect it. Then bisect the resulting segments. How many segments do you create? What is the measure of each segment? Chapter Assignments 73

14 12. Draw a 6-inch segment on the starter ray and draw the segment bisector. Repeat this process two more times. Bisect the results of the first bisection, and then bisect the results of the second bisections. (If you are not constructing with a straightedge and compass, then just use your ruler to bisect the 6-inch segment three times.) How many segments do you create? What is the measure of each segment? 74 Chapter Assignments

15 Assignment Assignment for Lesson.7 Name Date Warehouse Space Points of Concurrency in Triangles In the triangle below, construct the incenter, the circumcenter, the centroid, and the orthocenter. Label each center. Chapter Assignments 7

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