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Geometry Lesson 3-1: Identifying Lines and Angles

Learn about the relationships between lines and planes, including identifying parallel lines and planes, skew lines, and transversals. Study angle relationships formed by transversals, such as corresponding angles, alternate interior angles, and alternate exterior angles. Complete homework exercises to practice these concepts.

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Geometry Lesson 3-1: Identifying Lines and Angles

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  1. Geometry Lesson 3-1 Identify Lines and Angles

  2. Objectives • Previously we identified the relationship between two intersecting lines or two planes. • You will identify angle pair formed by three intersecting lines.

  3. Relationships b/w Lines and Planes • Parallel Lines: coplanar lines that do not intersect A B C D AB CD The symbol means is parallel to. Red arrows indicate lines are parallel

  4. Relationships b/w Lines and Planes (cont’d) • Parallel Planes: Planes that do not intersect. • Planes ABC and XYZ are parallel. • Skew Lines: Lines that do not intersect and are not coplanar. Work example 1 on page 147 A B D C W X Z Y

  5. Parallel and Perpendicular Postulates • If there is a line and a point not on that line then there is exactly one line through that point that is parallel to the given line. • If there is a line and a point not on that line then there is exactly one line through that point that is perpendicular to the given line. Example 2 on page 148

  6. Angle Relationships • Transversal: A line that intersects two or more lines in a plane at different points. l Line l is a transversal

  7. Angles formed by Transversals • Corresponding Angles: Are in corresponding positions (picture on pg. 149) • Alternate interior angles: Lie between the lines and are on opposite sides of the transversal. (picture on pg. 149) • Alternate exterior points: Lie outside the two lines and on opposite sides of the transversal. (picture on pg. 149) • Consecutive interior angles: Lie between the two lines and on the same side as the transversal. (picture on pg. 149) Work example 3 on page 149, also do guided practice for example 3

  8. 1, 2, 8, 7, 4, 3, 5, 6, 1, 5, 3, 5, 1, 7, 6, 3, 3, 7, 4, 8, 2, 8, 4, 5, 2, 6, 4, 6, Angle Relationships 1 2 4 3 5 6 8 7 Name Angles Exterior Angles Interior Angles Consecutive Interior Angles Alternate Exterior Angles Alternate Interior Angles Corresponding Angles

  9. 6 5 7 30 8 29 18 2 32 17 31 15 14 20 1 19 13 16 3 27 4 26 22 28 21 25 10 11 24 23 9 12 1.Name Your Category 2. Name a Pair that belongs in that Category

  10. Homework • Page 150-151 # 7-10, 18-23, 28, 29-32, 34-37

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