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Warm-Up

112 º. 138 º. Warm-Up. Find the measure of all angles possible. 1. 2. 2.6 Parallel Line Angles Objective. Be able to understand the angles made by parallel lines. Special Angles on Parallel Lines. Investigation 1) Angles on Parallel Lines

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Warm-Up

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  1. 112º 138º Warm-Up • Find the measure of all angles possible. 1. 2.

  2. 2.6 Parallel Line Angles Objective Be able to understand the angles made by parallel lines.

  3. Special Angles on Parallel Lines • Investigation 1) Angles on Parallel Lines • Step 1) Using a ruler, draw a pair of parallel lines on your paper. • Step 2) Draw a line that intersects both parallel lines (a transversal). Angles on Parallel Lines

  4. Special Angles on Parallel Lines • Step 3) Label the Angles 1-8 1 2 3 4 5 6 7 8

  5. Special Angles on Parallel Lines • Step 4) Place the patty paper over angles 1-4 and trace the intersecting lines and the four angles. 1 2 3 4

  6. Special Angles on Parallel Lines • Step 5) Slide the patty paper down to angles 5-8. What do you notice? 1 2 3 4

  7. 3 3 3 4 4 4 8 8 8 1 1 1 2 2 2 5 5 5 6 6 6 7 7 7 Special Angles on Parallel Lines Keyword Conjecture Sketch Corresponding Corresponding Angles are ___________. Angles (CA) Alternate Interior Alternate Interior angles are __________. Angles (AIA) Alternate Exterior Alternate Exterior angles are _________. Angles (AEA) congruent congruent congruent

  8. 3 3 4 4 8 8 1 1 2 2 5 5 6 6 7 7 Special Angles on Parallel Lines Keyword Conjecture Sketch Consecutive Interior Same Side Interior Angles Angles are _______________. Consecutive Exterior Same side exterior angles Angles are ______________. Parallel lines If two parallel lines are cut by a transversal, then Conjecture corresponding angles are ____________, alternate interior angles are ______________, and alternate exterior angles are ________________. supplementary supplementary congruent congruent congruent

  9. Special Angles on Parallel Lines Converse of Parallel Lines Conjecture • If 2 lines are cut by a transversal to form pairs of congruent Corresponding Angles, congruent Alternate Interior Angles, congruent Alternate Exterior Angles, supplementary Consecutive interior angles, or supplementary exterior angles, then the lines are ________________. parallel

  10. Converse l m 1 2 9 10 n 4 11 12 3 5 13 14 6 p 7 8 16 15

  11. Summary • Name four sets of angles formed by two parallel lines cut by a transversal • Name one set of supplementary angles formed by two parallel lines cut by a transversal.

  12. k s i d c j g 64 h 108 a b f e 75 m p 61 169 t 79 n Classwork: page 130 #7 copy the picture q

  13. Homework • Pg 129 #1-3, 9-15 • Pg. 140 #26

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