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Transcript

Geometry 3.1 Big Idea: Identify pairs of lines and angles Vocabulary Parallel Lines: Two lines that do not intersect and are coplanar. Skew Lines: Two lines that do not intersect and are not coplanar. Parallel Planes: Two planes that do not intersect. Ex: plane RSTU || plane WXYZ Note: a small triangle (like an arrow, pointed in one direction of a line) is used to indicate that lines are parallel (our book uses red color to denote this) – the arrow is on each line, not at the end Postulates 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 ║ to the given line. P m Postulate 14:Perpendicular Lines If there is a line and a point not on the line, then there is exactly one line through the point ┴ to the given line. P m More Vocabulary Transversal: A line that intersects 2 or more coplanar lines at different points. Corresponding Angles: on same side of transversal with same relationship (on top or on bottom) to other 2 lines (2 & 6), others? Alternate Interior Angles: Angles that lie between the 2 lines on opposite sides of the transversal (3 & 5), others? Alternate Exterior Angles: Angles that lie outside the 2 lines on opposite sides of the transversal. (2 & 8), others? Consecutive Interior Angles: Angles that lie between the 2 lines on the same side of the transversal.(4 & 5 ),others? Example: Identify all pairs of angles of the given type. • Corresponding • Alternate Interior 2 1 3 4 6 5 7 • Alternate Exterior 8 • Consecutive interior • Vertical