2. 7/4/20153-2: Angles and Parallel Lines1 12 34 78 65 l m t 12 34 78l m t 5 6

3. 7/4/20153-2: Angles and Parallel Lines2 Expectation: G1.1.1 : Solve multistep problems and construct proofs involving vertical angles, linear pairs of angles, supplementary angles, complementary angles, and right angles. G1.1.2: Solve multi-step problems and construct proofs involving corresponding angles, alternate interior angles, alternate exterior angles, and same-side (consecutive) interior angles.

4. 7/4/20153-2: Angles and Parallel Lines3 Parallel Lines and Angles Using the diagram on your graphic organizer, make conjectures about consecutive interior, corresponding, alternate interior and alternate exterior angles.

5. 7/4/20153-2: Angles and Parallel Lines4 Corresponding Angles Postulate If two parallel lines are cut by a transversal, then corresponding angles are ____________.

6. 7/4/20153-2: Angles and Parallel Lines5 Alternate Interior Angles l m t 12 3 4 5 6 78 Given: l || m Prove: ∠ 3 ≅ ∠ 6

7. 7/4/20153-2: Angles and Parallel Lines6

8. 7/4/20153-2: Angles and Parallel Lines7

9. 7/4/20153-2: Angles and Parallel Lines8 Alternate Interior Angle Theorem If two parallel lines are cut by a transversal, then alternate interior angles are _____________.

10. 7/4/20153-2: Angles and Parallel Lines9 l m t 12 3 4 5 6 78 If l // m, m ∠ 3 = 4x + 12 and m ∠ 6 = 9x – 18, determine the value of x and the measure of all 8 angles.

11. 7/4/20153-2: Angles and Parallel Lines10 Alternate Exterior Angle Theorem If two parallel lines are cut by a transversal, then alternate exterior angles are _____________.

12. 7/4/20153-2: Angles and Parallel Lines11 Consecutive Interior Angles l m t 12 3 4 5 6 78 Given: l || m Prove: ∠ 3 is ______________ ∠ 5

13. 7/4/20153-2: Angles and Parallel Lines12

14. 7/4/20153-2: Angles and Parallel Lines13

15. 7/4/20153-2: Angles and Parallel Lines14 Consecutive Interior Angle Theorem If two parallel lines are cut by a transversal, then consecutive interior angles are _________________.

16. 7/4/20153-2: Angles and Parallel Lines15 Consecutive Exterior Angle Theorem If two parallel lines are cut by a transversal, then consecutive exterior angles are _________________.

17. 7/4/20153-2: Angles and Parallel Lines16 l m t 12 3 4 5 6 78 If l // m, m ∠ 1 = 5x - 1 and m ∠ 7 = 6x - 39, determine the value of x and the measure of all 8 angles.

18. 7/4/20153-2: Angles and Parallel Lines17 Perpendicular Transversals l m t What is true about t and l ? Why?

19. 7/4/20153-2: Angles and Parallel Lines18 Perpendicular Transversal Theorem In a plane, if a transversal is perpendicular to one of 2 parallel lines, then it is _______________ to the other line as well.

20. 7/4/20153-2: Angles and Parallel Lines19 In the figure, BG // CE, BE //CD, BG bisects ∠ EBA, m ∠ 8 = 42 and m ∠ 3 = 18. Determine the measure of each angle.

21. 7/4/20153-2: Angles and Parallel Lines20 Determine the values of y and z.

22. In the figure showing ΔPQR below, line l is parallel to line m. Which one of the following angles must be congruent to ∠ y? A) ∠ 1 B) ∠ 2 C) ∠ 3 D) ∠ 4 E) ∠ 5 7/4/20153.3: Par allel Line s and Tra nsv ersa ls l m Q 1 2 y 345

23. 7/4/20153-2: Angles and Parallel Lines22 pages 135-137, #17- 25 (all), 39, 43 and 50 Assignment