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# Day 6. jp_1.4-1.5_angles_and_angle_pairs_ppt_

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### Day 6. jp_1.4-1.5_angles_and_angle_pairs_ppt_

1. 1. Angles and Angle Pairs<br />
2. 2. Angle Definition<br />Angle- <br /> is the union of two noncollinear rays that have a common endpoint.<br />
3. 3. Name that Angle!!!<br />D<br /> O G<br />D<br /> O G<br />D<br /> O G<br />D<br /> O G<br />D<br /> O G<br />D<br /> O G<br />D<br /> O G<br />D<br /> O G<br />D<br /> O G<br />D<br /> O G<br />D<br /> O G<br />4<br />
4. 4. What if we added ray OC<br />Is ∠O <br />still ∠DOG ?<br />C<br />D<br /> O G<br />D<br /> O G<br />D<br /> O G<br />D<br /> O G<br />D<br /> O G<br />D<br /> O G<br />D<br /> O G<br />D<br /> O G<br />D<br /> O G<br />D<br /> O G<br /> O G<br />∠O is nada<br />because:<br />∠COD ∠DOC<br />∠DOG ∠GOD<br />∠COG ∠GOC<br />
5. 5. Classifying Angles<br />
6. 6. Complementary Angles<br />60°<br />30°<br />Two angles that add up to 90°<br />X<br />25°<br />What is X?<br />X + 25 = 90<br />-25 -25<br />X = 65<br />
7. 7. Supplementary Angles<br />120°<br />60°<br />Two angles that add up to 180°<br />N<br />130°<br />x<br />M<br />G<br />A<br />m∠MAN + m∠NAG = 180<br />130 + X = 180<br />-130 = -130<br /> X = 50<br />
8. 8. Adjacent Angles<br />H<br />G<br />A<br />M<br />R<br />F<br />I<br />∠HAG and ∠MAG are adjacent angles because:<br />Share a common side<br />Share a common vertex<br />Are ∠RIG and ∠FIT adjacent angles?<br />NO! Common vertex , Yes Common side, No<br />G<br />T<br />
9. 9. Linear Pair<br />120°<br />60°<br />Adjacent Angles that are Supplementary<br />Is this a linear pair?<br />N<br />NO<br />M<br />G<br />A<br />m∠MAN + m∠NAG = 180<br />
10. 10. Are all linear pairs supplementary?<br /> YES<br />Are all supplementary angles linear pairs?<br />NO<br />40°<br />140°<br />
11. 11. 1<br />4<br />3<br />2<br />Vertical Angles<br /><1 and <2 are vertical angles<br /><3 and <4 are vertical angles<br />Vertical Angles are Congruent<br />
12. 12. t<br />m<br />n<br />Linear Pairs<br />Congruent or Supplementary ?<br />4x + 5x = 180<br />9x = 180<br />9x = 180 9 9<br />4x<br />5x<br />x = 20<br />4x<br />5x<br />4(20)<br />5(20)<br />100<br />80<br />80<br />100<br />
13. 13. t<br />m<br />n<br />Practice #1<br />Congruent or Supplementary ?<br />3x + 6x = 180<br />9x = 180<br />9x = 180 9 9<br />3x<br />6x<br />x = 20<br />3x<br />6x<br />3(20)<br />6(20)<br />120<br />60<br />120<br />60<br />
14. 14. t<br />m<br />n<br />Vertical angles<br />Congruent or Supplementary ? <br /> 3x + 20 = 7x - 8<br />-3x -3x<br /> 20 = 4x - 8<br /> +8 +8<br />28 = 4x 4 4<br />3x + 20<br />7 = x<br />7x - 8<br />3x + 20<br />7x - 8<br />3(7) + 20<br />7(7) - 8<br />41<br />41<br />41<br />41<br />
15. 15. t<br />m<br />n<br />Practice #2<br />Congruent or Supplementary ?<br />3x + 40 = 2x + 70<br />-2x -2x<br />x + 40 = 70<br />2x + 70<br />-40 = -40<br />x = 30<br />3x + 40<br />3x + 40<br />2x + 70<br />3(30) + 40<br />2(30) + 70<br />130<br />130<br />130<br />130<br />
16. 16. Summary<br />3x+10<br />CONGRUENT ANGLES<br />- SET THEM EQUAL<br /> 3x + 10 = x - 6<br />x - 6<br />SUPPLEMENTARY ANGLES<br /> -ADD TOGETHER and SET EQUAL to 180<br />6x + 3x = 180<br />6x<br />3x<br />