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Angles and Parallel Lines

2. 1. 4. 3. Angles and Parallel Lines. 6. 5. 8. 7. Transversal. Definition: A line that intersects two or more lines in a plane at different points is called a transversal. When a transversal t intersects line n and m , EIGHT angles are formed

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Angles and Parallel Lines

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  1. 2 1 4 3 Angles and Parallel Lines 6 5 8 7

  2. Transversal Definition:A line that intersects two or more lines in a plane at different points is called a transversal. When a transversal t intersects line n and m, EIGHTanglesare formed Exterior angles: Outside the lines Interior angles : Between the lines t m n

  3. Vertical Angles & Linear Pair Vertical Angles: Linear Pair: Two angles that are opposite angles. Vertical angles are congruent. 1  4, 2  3, 5  8, 6  7 Supplementary angles that form a straight line(sum = 180) 1 & 2 ,2 & 4 , 4 &3, 3 & 1, 5 & 6,6 & 8, 8 & 7, 7 & 5 1 2 3 4 5 6 7 8

  4. Corresponding Angles Corresponding Angles:Two angles, on the same side of the transversal, that occupy corresponding positions, one interior and one exterior.  2 and 6, 1 and 5,3 and 7,4 and 8 1 2 3 4 5 6 7 8

  5. Alternate Angles Alternate Interior Angles: Two angles that lie between the lines on opposite sides of the transversal (but not a linear pair). Alternate Exterior Angles: Two angles that lie outsidethe lines on opposite sides of the transversal. 3 and 6, 4 and5 2 and 7,1 and 8 1 2 3 4 5 6 7 8

  6. Consecutive Angles Consecutive Interior Angles: Two angles that lie betweenthe lines, both on the same side of the transversal. Consecutive Exterior Angles: Two angles that lie outsidethe lines, both on the same side of the transversal. 3 and 5 ,4 and 6 1 and 7 , 2 and 8 1 2 3 4 5 6 7 8

  7. Example List all pairs that fit the description Corresponding Alternate Exterior Alternate Interior Consecutive Interior < 4 and < 2 < 3 and < 1 < 5 and < 7 < 6 and < 8 < 4 and < 8 < 1 and < 5 < 2 and < 6 < 3 and < 7 < 3 and < 2 < 6 and < 7

  8. Example Complete the statement with corresponding, alternate exterior, alternate interior, or consecutive interior. < 4 and < 8 are < 2 and < 6 are < 1 and < 8 are < 7 and < 2 are < 4 and < 6 are < 5 and < 7 are Alternate interior Alternate exterior Consecutive interior Consecutive exterior Corresponding Vertical

  9. InvestigationLet’s check out therelationship of these angle pairs!

  10. Angles and Parallel Lines If two parallel lines are cut by a transversal, then the following pairs of angles are CONGRUENT. • Corresponding angles • Alternate interior angles • Alternate exterior angles If two parallel lines are cut by a transversal, then the following pairs of angles are SUPPLEMENTARY. • Consecutive interior angles • Consecutive exterior angles

  11. Example Given a ll b, find each measure given that m < 6 = 67°.

  12. Example State the postulate or theorem that justifies the statement.

  13. B A 1 2 10 9 12 11 4 3 C D 5 6 13 14 15 16 7 8 s t Example:If line AB is parallel to line CD and s is parallel to t, find the measure of all the angles when m< 1 = 100°. Justify your answers. m<2=80° m<3=100° m<4=80° m<5=100° m<6=80° m<7=100° m<8=80° m<9=100° m<10=80° m<11=100° m<12=80° m<13=100° m<14=80° m<15=100° m<16=80°

  14. B A 1 2 10 9 12 11 4 3 C D 5 6 13 14 15 16 7 8 s t Example: If line AB is parallel to line CD and s is parallel to t, find: 1. the value of x, if m<3 = 4x + 6 and the m<11 = 126. 2. the value of x, if m<1 = 100 and m<8 = 2x + 10. 3. the value of y, if m<11 = 3y – 5 and m<16 = 2y + 20. ANSWERS: 1. 30 2. 35 3. 33

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