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Angle Relationships in Parallel Lines

Learn to identify angle relationships in parallel lines and find missing angles. Understand concepts like corresponding angles, alternate interior angles, and more in Chapter 3. Explore examples of skew lines and transversals. Practice identifying and calculating angles in parallel line scenarios.

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Angle Relationships in Parallel Lines

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  1. 3.1 Angles and Parallel Lines SWBAT: identify angle relationships of parallel lines and find missing angles. Chapter 3: Parallel & Perpendicular Lines Chapter 3

  2. Warm UP • If y = 2x + 1, write an equation of a line that is parallel and a line that is perpendicular. • Define parallel in your own words. • Give an example of skew lines.

  3. Homework • Page 150 # 12-36 even (Identifying Angle Relationships) • Monday is Portfolio Day- please bring the portfolio you were given yesterday to class

  4. 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 (same side) interior angles Alternative exterior angles Alternative interior angles Corresponding angles t m n

  5. Vertical Angles & Linear Pair Two angles that are opposite angles. Vertical angles are congruent. Vertical Angles: Linear Pair: 1  4, 2  3, 5  8, 6  7 Supplementary angles that form a 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

  6. Corresponding Angles Corresponding Angles: Two angles that occupy corresponding positions.  2  6, 1  5,3  7,4  8 1 2 3 4 5 6 7 8

  7. Consecutive (Same Side) Angles Consecutive (Same Side) Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal. Consecutive (Same Side) Exterior Angles: Two angles that lie outside parallel lines on the same sides of the transversal. m3 +m5 = 180º, m4 +m6 = 180º 1 2 m1 +m7 = 180º, m2 +m8 = 180º 3 4 5 6 7 8

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

  9. 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 (same side) interior angles • Consecutive (same side) exterior angles Continued…..

  10. 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°

  11. Classwork: Congruent or Supplementary? • Parallel Lines Worksheet: • Vertical angles are ___________. • Same side exterior angles are _______. • Alternate interior angles are ________. • Alternate exterior angles are ________. • Corresponding angles are __________. • In pairs, find the measures a-g and 1-15

  12. Homework • Page 150 # 12-36 even (Identifying Angle Relationships)

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