Warm-Up

2.6 Parallel Line Angles Objective Explore relationships of the angles formed by a transversal cutting parallel lines. HW: p. 141 #1, 3-6, 9-10 (DUE Tuesday 9/29)

Investigation “Which angles are congruent?”  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).

 Step 3) Label the Angles

 Step 4) Place the patty paper over angles 1-4 and trace the intersecting lines and the four angles

 Step 5) Slide the patty paper down to angles 5-8. What do you notice? 12 43

Transveral

Special Angles on Parallel Lines KeywordConjectureSketch Corresponding Corresponding Angles are ___________. Angles (CA) Alternate InteriorAlternate Interior angles are __________. Angles (AIA) Alternate ExteriorAlternate Exterior angles are _________. Angles (AEA) congruent

Special Angles on Parallel Lines KeywordConjectureSketch Consecutive Interior Same Side Interior Angles Angles are _______________. Consecutive ExteriorSame side exterior angles Angles are ______________. Parallel lines If two parallel lines are cut by a transversal, then Conjecturecorresponding angles are ____________, alternate interior angles are ______________, and alternate exterior angles are ________________. supplementary congruent

Special Angles on Parallel Lines  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 ________________. Converse of Parallel Lines Conjecture parallel BASICALLY: IF ALL THE ANGLS ARE CONGRUENT, THEN THE LINES ARE PARALLEL

Practice Time!

1) Find the missing angle. 36° ?°?°

1) Find the missing angle. 36° ?°?° 90 ° – 36 = 54°

2) Find the missing angle. 64° ?°?°

2) Find the missing angle. 64° ?°?° 90 ° – 64° = 26°

3) Solve for x. 3x° 2x°

3) Solve for x. 3x° 2x° 3x° + 2x° = 90° 5x = 90 x =18

4) Solve for x. 2x + 5 x + 25

4) Solve for x. 2x + 5 x + 25 (2x + 5) + (x + 25) = 90 3x + 30 = 90 3x = 60 x = 20

5) Find the missing angle. ?°?° 168°

5) Find the missing angle. ?°?° 168° 180° – 168° = 12°

6) Find the missing angle. 58° ?°?°

6) Find the missing angle. 58° ?°?° 180° – 58° = 122°

7) Solve for x. 4x 5x

7) Solve for x. 4x 5x 4x + 5x = 180 9x = 180 x = 20

8) Solve for x. 2x x + 20

8) Solve for x. 2x x + 20 (2x + 10) + (3x + 20) = 180 5x + 30 = 180 5x = 150 x = 30

9) Lines l and m are parallel. l || m Find the missing angles. 42° l m b°b° d°d° f°f° a ° c°c° e°e° g°g°

9) Lines l and m are parallel. l || m Find the missing angles. 42° l m 138°

10) Lines l and m are parallel. l || m Find the missing angles. 81° l m b°b° d°d° f°f° a ° c°c° e°e° g°g°

10) Lines l and m are parallel. l || m Find the missing angles. 81° l m 99°

x + (2x + 45) = 180 3x + 45 = 180 3x = 135 x = 45

11) Find the missing angles. 70 ° b° 70 ° d °65 ° Hint: The 3 angles in a triangle sum to 180°.

11) Find the missing angles. 70 ° 40° 70 ° 75 °65 ° Hint: The 3 angles in a triangle sum to 180°.

12) Find the missing angles. 45 ° b° 50 ° d °75 ° Hint: The 3 angles in a triangle sum to 180°.

12) Find the missing angles. 45 ° 85° 50 ° 20°75 ° Hint: The 3 angles in a triangle sum to 180°.

In the figure a || b. 13. Name the angles congruent to  Name all the angles supplementary to  If m  1 = 105° what is m  3? 16. If m  5 = 120° what is m  2?  1,  5,  7  1,  3,  5,  7 105° 60°

The End

Exit Ticket 2.6 q a c k s d 108 g h j i f e b 61 t 75 m n p 79