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Geometry

In this lesson, you will explore the relationships of lines and angles, including parallel lines and transversals. You will learn about corresponding angles, alternate exterior angles, alternate interior angles, and consecutive interior angles.

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Geometry

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

  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. 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: Real Life Ex:

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

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

  9. 1 2 43 5 6 87 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 6 5 7 8

  10. 1 2 43 5 6 87 3.1 Lines and Angles Alternate Exterior Angles: angles on opposite sides of the transversal that are both exterior Examples: <1 and <7, <2 and <8 2 1 8 7

  11. 1 2 43 6 5 87 3.1 Lines and Angles Alternate Interior Angles: angles on opposite sides of the transversal that are both interior Examples: <3 and <5, <4 and <6 4 3 6 5

  12. 1 2 43 5 6 87 3.1 Lines and Angles Consecutive Interior Angles: angles on the same side of the transversal, both interior Examples: <3 and <6, <4 and <5 4 3 6 5

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

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

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

  16. a 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 5 12 11 6 c 8 7

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

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