2. Daily Check Daily Check 1.Name the type of angles. (1 point each) a) b) 1 2 21 2.Solve for x. (4 points each) a) b) and are complementary. 10x-10 4x+22

3. CCGPS Analytic Geometry Day 5 (8-8-14) UNIT QUESTION: How do I prove geometric theorems involving lines, angles, triangles and parallelograms? Standards: MCC9-12.G.SRT.1-5, MCC9-12.A.CO.6-13 Today’s Question: Which angles are congruent to each other when parallel lines are cut by a transversal? Standard: MCC9-12.A.CO.9

4. Parallel Lines and Transversals

5. Parallel Lines – Two lines are parallel if and only if they are in the same plane and do not intersect. A B C D AB  CD

6. Parallel Planes – Planes that do not intersect.

7. Skew Lines – two lines that are NOT in the same plane and do NOT intersect

8. Ex 1: Name all the parts of the prism shown below. Assume segments that look parallel are parallel. A B C D E F G 1. A plane parallel to plane AFE. Plane BGD 2. All segments that intersect GB. AB, FG, DG, BC 3. All segments parallel to FE. GD, BC 4. All segments skew to ED. BG, FA, BC

9. Transversal – A line, line segment, or ray that intersects two or more lines at different points. a b t Line t is a transversal.

10. Special Angles 1 2 3 4 5 6 7 8 Interior Angles – lie between the two lines (  3,  4,  5, and  6) Alternate Interior Angles – are on opposite sides of the transversal. (  3 &  6 AND  4 and  5) Consecutive Interior Angles – are on the same side of the transversal. (  3 &  5 AND  4 &  6)

11. 6 5 4 3 More Special Angles 2 1 7 8 Exterior Angles – lie outside the two lines (  1,  2,  7, and  8) Alternate Exterior Angles – are on opposite sides of the transversal (  1&  8 AND  2 &  7)

12. Ex. 2: Identify each pair of angles as alternate interior, alternate exterior, consecutive interior, or vertical. 1 2 3 4 5 6 7 8 a.  1 and  2 b.  6 and  7 c.  3 and  4 d.  3 and  8 Alt. Ext. Angles Vertical Angles Alt. Int. Angles Consec. Int. Angles

13. Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then each pair of alternate interior angles are congruent. 2 1 3 4 5 6 7 8  2   6  3   7

14. Alternate Exterior Angles Theorem If two parallel lines are cut by a transversal, then each pair of alternate exterior angles are congruent. 2 1 3 4 5 6 7 8  1   5  4   8

15. Consecutive Interior Angles Theorem If two parallel lines are cut by a transversal, then each pair of consecutive interior angles are supplementary. 2 1 3 4 5 6 7 8 m  2 + m  3 = 180° m  6 + m  7 = 180°

16. Ex. 3 In the figure, p  q. If m  5 = 28°, find the measure of each angle. 2 1 3 4 5 6 7 8 a. m  8 = b. m  1 = c. m  2 = d. m  3 = e. m  4 = 28° 152° 28° p q

17. Ex. 4 In the figure, s  t. Find the m  CBG. S t 3x -5 4x -29 A B C D E F G 3x – 5 = 4x - 29 -5 = x - 29 24 = x Step 1: Solve for x. Step 2: m  CBG = m  ABE = 3x -5. 3x-5 = 3(24) – 5 = 72-5 = 67°

18. Ex: 5 Identify each pair of angles as: alt. interior, alt. exterior, consecutive interior, or vertical. 1 16 2 15 11 10 12 9 13 8 6 7 3 14 4 5

19. Ex: 6 Identify each pair of angles as: alt. interior, alt. exterior, consecutive interior, or vertical. 1 16 2 15 11 10 12 9 13 8 6 7 3 14 4 5

20. Ex: 7 Identify each pair of angles as: alt. interior, alt. exterior, consecutive interior, or vertical. 1 16 2 15 11 10 12 9 13 8 6 7 3 14 4 5

21. Ex: 8 Identify each pair of angles as: alt. interior, alt. exterior, consecutive interior, or vertical. 1 16 2 15 11 10 12 9 13 8 6 7 3 14 4 5

22. Ex: 9 Identify each pair of angles as: alt. interior, alt. exterior, consecutive interior, or vertical. 1 16 2 15 11 10 12 9 13 8 6 7 3 14 4 5

23. Ex: 10 Identify each pair of angles as: alt. interior, alt. exterior, consecutive interior, or vertical. 1 16 2 15 11 10 12 9 13 8 6 7 3 14 4 5