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Agenda 3/13 & 3/14

Agenda 3/13 & 3/14. Warm – Up Go over homework More special angles Mixin’ in some equations Making sure the lines are parallel Parallel Lines and Ratio Segments Homework Assignment Quiz Time. Warm - UP. 1. What is the slope of the line parallel to:

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Agenda 3/13 & 3/14

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  1. Agenda 3/13 & 3/14 • Warm – Up • Go over homework • More special angles • Mixin’ in some equations • Making sure the lines are parallel • Parallel Lines and Ratio Segments • Homework Assignment • Quiz Time

  2. Warm - UP 1. What is the slope of the line parallel to: a. y =1/3x + 4 b. y = -x + 8 m = 1/3 m = -1 2.What is the slope of the line perpendicular to: a. y =1/3x + 4 b. y = -x + 8 m = - 3 (opposite recip.) m = 1 3. Shane has sketched a house on graph paper as a blue print. The coordinates of the base of the house are (2,-1); (4,0); (2,4); (0,3). Are the walls perpendicular? no

  3. Go Over Homework • Date: 2/13 Homework: 11 • Base: 70 (-5) 14 problems total • a)﬩ b) || c) neither d) ﬩ • a) points are plotted on a graph… b) -1 and -1 c) 1 and 1 d) they are perpendicular e) It is 90° f) They are parallel 3. y = ½ x + 7 4. y = 4x + 9 5. y = ¼ x – 8 6. y = -3/2 x – 4

  4. More Special Angles • Complementary Angles These are 2 angles whose measures add up to 90 degrees. • Supplementary Angles These are 2 angles whose measures add up to 180. (Hmmm…where have you seen that number before?)

  5. More Special Angles

  6. Name the angles that are congruent to angle 5. Angles 1,4,8 Name the angles that are supplementary to angle 3. angles 1,4,6,7 More Special Angles

  7. Solve for x, if <1 = 119 and <8 = 4x + 7. <1 = <8 so… 119 = 4x+7 112 = 4x 28 = x 2) If <1= 4x + 4 and its adjacent angle is 100, what is the value of x?<1 + adj angle=180 4x + 4 + 100 = 180 4x + 104 = 180 4x = 76 x = 19 Mixin’ in Some Equations

  8. 3) If <4 = 99 degrees and <5=2c + 17, what is c? <4 = <5 99 = 2c + 17 82 = 2c 41 = c 4) If <2=1/2 x -10 and <7=83, what is x? <2 = <7 ½ x - 10 = 83 ½ x = 93 X = 186 Mixin’ in Some Equations

  9. Making Sure the Lines are Parallel We said, the other day, that if 2 parallel lines were crossed by a transversal the resulting pairs of angles were congruent: • Corresponding angles • Alternate Interior angles • Alternate Exterior angles We also said that consecutive interior angles had a sum of 180 (supplementary angles).

  10. Making Sure the Lines are Parallel We can say the converse, (the opposite), of this is true. If the ________ pairs are congruent, the lines are parallel. The following can go in the blank: corresponding angles, alternate interior angles, alternate exterior angles If the consecutive interior angles are supplementary the lines are parallel.

  11. Making Sure the Lines are Parallel Determine if lines r and s are parallel… 1)no, the alt ext angles 2) yes, the corr. <‘s 3) yes the angles are not congruent are congruent add up to 180.

  12. Making Sure the Lines are Parallel Determine if lines r and s are parallel… 4) no, this angle pair 5) vertical angles 6) Name 3 ways to Does not workdo not prove || linesprove 2 lines cut by a transversal are parallel.

  13. Parallel Lines and Ratio Segments When 2 parallel lines are cut by a transversal, proportional segments are formed. 3 = 2 or 3 = 6 • 4 2 4 Top 1= top 2 or top 1 = bottom 1 Bottom 1 bottom 2 top 2 = bottom 2

  14. Parallel Lines and Ratio Segments We can use proportions to help find missing lengths of sides. 24 = x 36 24 24(24) = 36 x 576 = 36 x 16 = x

  15. Find x. 15 = 10 x 6 15(6) =10x 90 = 10x 9 = x Solve for x and y. 6 = 106 = 10 X 8 y 6 6(8) = 10x 6(6) = 10y 48 = 10x 36 = 10y 4.8 = x 3.6 = y Parallel Lines and Ratio Segments

  16. Parallel Lines and Ratio Segments • A little tougher.. Find x. 24 = x 36 80 -x 24(80-x) = 36x 1920 -24x =36x 1920 = 60x 32 = x this would be 80-x

  17. Now here is an application problem for you… See next Slide for solution

  18. Okay, this is a bit of a challenge… 1)Let’s work on find the first lot. Get rid of y and z, by calling it 600 – x and add the “tops” for y and z (150 + 100 = 250) Use the proportion: 200 / x = 250 / 600 – x 200 (600 – x) = 250 x 120000 – 200x = 250x 120000 = 450x 266.67 = x 2) Now let’s find y: 200 / 266.67 = 150 / y 200 y = 266.67(150) 200y = 40000 y = 200

  19. Now for the last side : 200 / 266.67 = 100 / z 200 z = 266.67(100) 200 z = 26667 z = 133.33 Done! – no this will not be on the test, but this IS where it is used in the real world.

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