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Transcript

3.1 Notes Identify Pairs of Lines and Angles Geometry Two lines that do not intersect are either ______________ or __________. _____________ are coplanar, and ______________ are not coplanar. Two lines in the same plane are either _____________ or ____________ in one point. If two lines intersect at a 90 degree angle, then the two lines are _____________. Two planes that do not intersect are ______________. t n j k Example 1: Identify relationships in space. Think of each segment in the picture as part of a line. Which line(s) or plane(s) appear to fit the description? a.) Line(s) parallel to ED and containing point C. b.) Line(s) skew to ED . c.) Line(s) perpendicular to ED . d.) Plane(s) parallel to plane ABH. Parallel Postulate Perpendicular Postulate ●P ●P Given line l and point P, there is exactly one line through P that is ____________ to line l. Given line l and point P, there is exactly one line through P that is ______________ to line l. Example 2: Use the diagram to answer each question. a.) Name a pair of parallel lines. b.) Name a pair of perpendicular lines. c.) Is AB BC ? Explain. RECALL: Vertical Angles are formed by two pairs of opposite rays. 1 4 2 3 Transversal: A line that ________________ two or more _________________ lines at different points. ANGLES FORMED BY TRANSVERSALS Alternate Interior Angles: Lie between the two Corresponding Angles: Have corresponding positions. lines on opposite sides of the transversal. 2 4 6 5 t t Alternate Exterior Angles: Lie outside of the Consecutive Interior Angles: Lie between the two lines on opposite sides of the transversal. two lines on the same side. 2 3 7 5 t t Example 3: Identify all pairs of angles of the given type. a.) Corresponding b.) Alternate Interior c.) Alternate Exterior d.) Consecutive Interior e.) Vertical 1 2 3 4 7 5 6 8