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Angles and Parallel Lines

Angles and Parallel Lines. 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 of the following types are formed: Exterior angles Interior angles

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Angles and Parallel Lines

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  1. Angles and Parallel Lines

  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, eight angles of the following types are formed: Exterior angles Interior angles Consecutive angles Alternate angles t m n

  3. Corresponding Angles Corresponding Angles: Two angles that occupy corresponding positions. Corresponding Angles Postulate: If two parallel lines are cut by a transversal, then the Corresponding angles are congruent.  2  6, 1  5,3  7,4  8 1 2 3 4 5 6 7 8

  4. Same Side or Consecutive Angles Consecutive Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal. Consecutive Interior Angles Theorem: If two parallel lines are cut by a transversal, then the Consecutive Interior Angles are supplementary. m3 +m5 = 180º, m4 +m6 = 180º 1 2 3 4 5 6 7 8

  5. Same Side or Consecutive Angles Consecutive Exterior Angles: Two angles that lie outside parallel lines on the same sides of the transversal. Consecutive Exterior Angles Theorem: If two parallel lines are cut by a transversal, then the Consecutive Exterior Angles are supplementary. m1 +m7 = 180º, m2 +m8 = 180º 1 2 3 4 5 6 7 8

  6. Alternate Angles • Alternate Interior Angles: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair). • Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, then the Alternate Interior Angles are congruent. 3  6,4  5 1 2 3 4 5 6 7 8

  7. Alternate Angles • Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal. • Alternate Exterior Angles Theorem: If two parallel lines are cut by a transversal, then the Alternate Exterior Angles are congruent. 2  7,1  8 1 2 3 4 5 6 7 8

  8. 2 60° 1 4 3 Example 1 • Find all numbered angles Angles and Parallel Lines

  9. 30 A B 5y 2x (x-y) D C Example 2 • Find x and y Angles and Parallel Lines

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