Topic: Use Parallel Lines and Transversals. and transversals?

Transcription

1 Topic: Use Parallel Lines and Transversals and transversals? Get a calculator, protractor and handouts from the back of the room Fill out your assignment sheet Have your Homework out to be graded Do the warm-up on the guided notes page 1

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3 Warm-up 3

4 Homework Answers 4

5 27) Corresponding 28) Alternate-interior 29) Same-side interior or Consecutive 5

6 Assignment a b c ) Which line is a transversal? 2) Which angles are Corresponding Angles? 3) Which angles are Alternate Interior Angles? 4) Which angles are Alternate Exterior Angles? 5) Which angles are Same- Side interior angles? 6) If we think about some things we learned in Algebra, one was about the concept of slope. What is the slope of a line? 7) What are some ways we can find the slope of a line? 8) Using on of those methods, determine the slope of lines b and c? Slope of Line b = Slope of Line c = 9) What do you notice about the slope of lines b and c? 10) Are lines b and c coplanar? 11) In Algebra one, you should have also learned that if two lines are coplanar and have the same slope, then the two lines are. 6

7 Now measure using a protractor the size of angles 1 through 8. Please list the angles sizes below in the space provided. m<1 = m<5 = m<2 = m<6 = m<3 = m<7 = m<4 = m<8 = Corresponding Angle Pairs Alternate Interior Angles m<1 =, m<5 = m<3 =, m<6 = m<3 =, m<7 = m<4 =, m<5 = m<2 =, m<6 = m<4 =, m<8 = Same-side Interior Angles Alternate Exterior Angles m<3 =, m<5 = m<1 =, m<8 = m<4=, m<6 = m<2 =, m<7 = 12) What do you notice about the size of all of the pairs of corresponding, alternate interior, and alternate exterior angles? 13) What do you notice about the sets of same side interior angles? 7

8 Now we will repeat the exercise with a different set of lines d, e and f. d e f ) Which line is a transversal? 15) Find the slopes of lines e and f? 16) Are the slopes of e and f the same or different? 17) Therefore, since the slopes of lines e and f are not the same, then line e is not to line f. 8

9 Now measure using a protractor the size of angles 1 through 8. Please list the angles sizes below in the space provided. m<1 = m<5 = m<2 = m<6 = m<3 = m<7 = m<4 = m<8 = Corresponding Angle Pairs Alternate Interior Angles m<1 =, m<5 = m<3 =, m<6 = m<3 =, m<7 = m<4 =, m<5 = m<2 =, m<6 = m<4 =, m<8 = Same-side Interior Angles Alternate Exterior Angles m<3 =, m<5 = m<1 =, m<8 = m<4=, m<6 = m<2 =, m<7 = Are the pairs of corresponding, alternate interior, and exterior angles congruent?? Are the pairs of Same-side interior angles supplementary?? Why do you believe this is so? What was different about the first picture and the second picture? In summary If two lines are cut (intersected) by a transversal, and the two lines are parallel, then Corresponding angles are Alternate Interior angles are Alternate Exterior angles are Same-side interior angles are If two lines are cut (intersected) by a transversal, and the two lines are not parallel, then Corresponding angles are Alternate Interior angles are Alternate Exterior angles are Same-side interior angles are 9

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14 If two parallel lines are cut by a transversal, then 1) Corresponding angles are congruent 2) Alternate Interior angles are congruent 3) Alternate Exterior angles are congruent 4) Same-Side Interior angles are supplementary. Any two angles in this picture have to be congruent or Add to 180 degrees. Which angles have to be congruent to angle 1? Which angles have to be congruent to angle 2? Are angles <1 and < 5 congruent or supplementary? Are angles <2 and < 8 congruent or supplementary? 14

15 1) Example 3 6x 4x-20 15

16 Example 4 3x-30 2x+20 Example 5 4x+12 7x-24 Example 6 4x+12 6x-32 16

17 Example 7 Find x, y and z Find the angle measures 8) 9) 10) 11) 17

18 Homework: Pg # 6-11, 13-23, all 18

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