1. Name the type of angles. (1 point each) a) b)
Session 3 Warmup Quiz 9-17
Name the type of angles. (1 point each)
a) b) 1 2 1 2
Solve for x. (4 points each) a)
b) and are complementary.
4x+22
10x-10

2. Homework Review

3. CCGPS Analytic Geometry Day 3 (9-17-13)
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. B A D C
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
Ex 1: Name all the parts of the prism shown below. Assume segments that look parallel are parallel.
1. A plane parallel to plane AFE. F E
Plane BGD G D
2. All segments that intersect GB. A
AB, FG, DG, BC C B
GD, BC
3. All segments parallel to FE.
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.b
Line t is a transversal. t

10. Special Angles 2 1 4
Interior Angles – lie between the two lines (3, 4, 5, and 6) 3 6 5 8 7
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. More Special Angles
Exterior Angles – lie outside the two lines (1, 2, 7, and 8) 2 1 4 3 6 5 8 7
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.
a. 1 and 2 1
Alt. Ext. Angles 6 7 3
b. 6 and 7 4 8 5
Vertical Angles 2
c. 3 and 4
Alt. Int. Angles
d. 3 and 8
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. 8 1 7
2  6 2 6 3 5 4
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. 8 1 7
1  5 2 6 3 5 4
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.
m2 + m3 = 180° 8 1 7 2 6
m6 + m7 = 180° 3 5 4

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

17. Ex. 4 In the figure, st. Find the mCBG.A
Step 1: Solve for x. G S B D
3x – 5 = 4x - 29
3x -5 C
-5 = x - 29
4x -29 E
24 = x F
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
Ex: 5 Identify each pair of angles as: alt. interior, alt. exterior, consecutive interior, or vertical. 10 11 9 12 16
alternate
exterior 8 1 15 13 7 2 6 14 3 5 4

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

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

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

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

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