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Understanding Lines and Angles in Geometry

Learn about pairs of lines and angles, including parallel, skew, corresponding, alternate interior, and exterior angles. Explore key concepts and postulates in geometry.

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Understanding Lines and Angles in Geometry

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  1. Geometry: Chapter 3 Ch. 3.1: Identify Pairs of Lines and Angles

  2. Two lines that do not intersect are either parallel lines or skew lines. Two lines are parallel lines if they do not intersect and are coplanar. Two lines are skew lines if they do not intersect and are not coplanar. Two planes that do not intersect are parallel planes.

  3. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 147.

  4. Parallel and Perpendicular Lines. Two lines in the same plane are either parallel or intersect in a point. Through a point not on a line, there are infinitely many lines. Exactly one of these lines is parallel to the given line, and exactly one of them is perpendicular to the given line.

  5. Postulate 13: Parallel Postulate If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line. There is exactly one line through P parallel to l. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 147.

  6. Postulate 14: Perpendicular Postulate If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line. There is exactly one line through P perpendicular to l. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 147.

  7. Ex. 2. The figure shows a swing set on a playground. • Name a pair of perpendicular lines • Name a pair of parallel lines. • Is line DH perpendicular to line LM? Explain. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 148.

  8. ANGLES AND TRANSVERSALS: A transversal is a line that intersects two or more coplanar lines at different points.

  9. KEY CONCEPTS: Angles Formed from TRANSVERSALS Two angles are called corresponding angles if they have corresponding positions. For example, 2 and 6 are above the lines and to the right of the transversal t. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 149.

  10. Angles Formed from TRANSVERSALS Two angles are called alternate interior angles if they lie between the two lines and on opposite sides of the transversal t. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 149.

  11. Angles Formed from TRANSVERSALS Two angles are called alternate exterior angles if they lie outside the two lines and on opposite sides of the transversal. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 149.

  12. Angles Formed from TRANSVERSALS Two angles are called consecutive interior angles if they lie between the two lines and on the same side of the transversal. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 149.

  13. Ex. 3. Identify all pairs of angles of the given type. • Corresponding • Alternate interior • Alternate exterior • Consecutive interior Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 149.

  14. Go to: http://www.classzone.com/cz/books/geometry_2007_na/get_chapter_group.htm?cin=3&rg=help_with_the_math&at=powerpoint_presentations&var=powerpoint_presentations Ch. 3, Lesson 1, Ex. 3 for extra practice

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