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3-1 Lines and Angles

3-1 Lines and Angles. Parallel and Skew. Parallel lines are coplanar lines that do not intersect. The symbol  means “is parallel to”. Skew lines are noncoplanar ; they are not parallel and do not intersect.

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3-1 Lines and Angles

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  1. 3-1 Lines and Angles

  2. Parallel and Skew • Parallel lines are coplanar lines that do not intersect. • The symbol  means “is parallel to”. • Skew lines are noncoplanar; they are not parallel and do not intersect. • Parallel planes are planes that do not intersect. • A line and a plane can be parallel; segments and rays can be parallel or skew.

  3. Identifying Nonintersecting Lines and Planes • Which segments are parallel to AB? • Which segments are skew to CD? • What are two pairs of parallel planes? • What are two segments parallel to plane BCGF? • Why are FE and CDnot skew?

  4. Angles Pairs Formed by Transversals 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 A transversal is a line that intersects two or more coplanar lines at different points (line t). Two angles are corresponding angles if they occupy corresponding positions (1 and 5, 3 and 7, 2 and 6, 4 and 8). Two angles are alternate exterior angles if they lie outside the two lines on opposite sides of the transversal (1 and 8, 2 and 7). Two angles are alternate interior angles if they lie between the two lines on opposite sides of the transversal (3 and 6, 4 and 5). Two angles are consecutive (or same side) interior angles if they lie between the two lines on the same side of the transversal (3 and 5, 4 and 6). 5 5 5 5 5 6 6 6 6 6 7 7 7 7 7 8 8 8 8 8 t t

  5. Identifying an Angle Pair • Identify all pairs of angles with the following relationships: • Alternate interior • Same-side interior • Corresponding • Alternate exterior

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