1. Geometry
Unless you try to do something beyond what you have already mastered, you will never grow.
Ralph Waldo Emerson
Today:
Chapter 2 Check
3.1 Instruction
Practice

2. Warm Up How many degrees are in a triangle?
What is the relationship between these 2 angles?
Name the relationship between 1 and 2. 1 2

3. You used angle and line segment relationships to prove theorems.
Identify relationships between two lines or two planes.
Name angle pairs formed by parallel lines and transversals.
Then/Now

4. Mathematical Practices
Content Standards
G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
CCSS

5. 3.1 Lines and Angles Objectives: Identify the relationships of lines
Identify angles formed by transversals
Vocabulary:
Parallel, perpendicular, skew, transversal, corresponding angles, alternate exterior angles, alternate interior angles, consecutive interior angles

6. 3.1 Lines and Angles Vocabulary: Parallel: Parallel Planes:
Real Life Ex:
Parallel Lines:

7. 3.1 Lines and Angles Vocabulary: Perpendicular: Real Life Ex:
Transversal:
Skew:

8. n b a 2 1 3 4 6 5 8 7 Which line is a transversal? Angle Types:
Interior: 3, 4, 5, 6
Exterior: 1, 2, 7, 8

9. 3.1 Lines and Angles
Corresponding Angles: angles that occupy corresponding position. Same side of transversal, one on the interior and one on the exterior.
Examples: <1 and < 5, <2 and <6, <3 and <7, <4 and <8 1 2 5 6 1 2 4 3 6 5 7 8

10. 3.1 Lines and Angles
Alternate Exterior Angles: angles on opposite sides of the transversal that are both exterior 1 2 5 6 1 2 8 7
Examples: <1 and <7, <2 and <8

11. 3.1 Lines and Angles
Alternate Interior Angles: angles on opposite sides of the transversal that are both interior 1 2 5 6 4 3 6 5
Examples: <3 and <5, <4 and <6

12. 3.1 Lines and Angles
Consecutive Interior Angles: angles on the same side of the transversal, both interior 1 2 5 6 4 3 6 5
Examples: <3 and <6, <4 and <5

13. a b c 1 2 4 3 9 10 12 5 11 6 8 7 <3 and <9, <4 and <10
Find:
Alternate interior angles b 1 2 4 3 9 10 12 5 11 6 c 8 7
Need to focus on one transversal at a time!!!!!
<3 and <9, <4 and <10

14. a b c 1 2 4 3 9 10 12 5 11 6 8 7 <3 and <6, <2 and <5
Find:
Alternate interior angles b 1 2 4 3 9 10 12 5 11 6 c 8 7
NEXT TRANSVERSAL!
<3 and <6, <2 and <5

15. a b c 1 2 4 3 <5 and <11, <8 and <10 9 10 12 5 11 6 8 7
Find:
Alternate interior angles b 1 2 4 3
<5 and <11, <8 and <10 9 10 12 5 11 6 c 8 7
LAST TRANSVERSAL!

16. a b c Total: <3 and <9, <4 and <10, 1 2
Find:
Alternate interior angles b
Total:
<3 and <9, <4 and <10,
<3 and <6, <2 and <5,
<5 and <11, <8 and <10 1 2 4 3 9 10 12 5 11 6 c 8 7

17. Geometry
Unless you try to do something beyond what you have already mastered, you will never grow.
Ralph Waldo Emerson
Assignment:
3.1 p. 175 #1-3, 9-12, 55