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Chapter 3: Parallel & Perpendicular Lines

3.1 Angles and Parallel Lines SWBAT: identify angle relationships of parallel lines and find missing angles. Chapter 3: Parallel & Perpendicular Lines. Chapter 3. Warm UP. If y = 2x + 1, write an equation of a line that is parallel and a line that is perpendicular.

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Chapter 3: Parallel & Perpendicular 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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