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

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

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

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

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

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

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

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

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 4 3 5 8 7 6 1 2 4 3 6 5 7 8

3.1 Lines and Angles Alternate Exterior Angles: angles on opposite sides of the transversal that are both exterior 1 2 4 3 5 8 7 6 1 2 8 7 Examples: <1 and <7, <2 and <8

3.1 Lines and Angles Alternate Interior Angles: angles on opposite sides of the transversal that are both interior 1 2 4 3 5 8 7 6 4 3 6 5 Examples: <3 and <5, <4 and <6

3.1 Lines and Angles Consecutive Interior Angles: angles on the same side of the transversal, both interior 1 2 4 3 5 8 7 6 4 3 6 5 Examples: <3 and <6, <4 and <5

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

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

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!

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

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