Geometry Chapter 3, Section 1 Lines and Angles Geometry Chapter 3, Section 1

Notes What does it mean for two lines to be parallel? Parallel lines: Lines that do not intersect and are coplanar. What about lines that do not intersect and are not coplanar? Skew Lines: Lines that do not intersect and are not coplanar. What does it mean for two planes to be parallel? Parallel Planes: planes that do not intersect. Example: the planes containing the ceiling and floor are parallel

Notes 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. Parallel lines have the same slope (line P slope = 3 and Line m slope = 3) Tilted at the same angle 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. Perpendicular lines have slopes that are negative reciprocals (line k slope = 4 and line Q slope = – 1/4) At 90 degrees from each other

Notes Transversal: a line that intersects two or more lines in a plane at different points. E.g. Line c is a transversal to lines a and b. Line b is a transversal to which two other lines? a & c How about line a? b & c When a transversal intersects two lines, how many angles are formed? 8 angles are formed

Notes Angles formed by a transversal. We give certain pairs of these angles special names. Exterior Angles: 1, 2, 7, & 8 Interior Angles: 3, 4, 5, 6 Corresponding Angles: 1 & 5 ; 2 & 6 ; 3 & 7 ; 4 & 8 Alternate Exterior Angles: 1 & 8 ; 2 & 7 Alternate Interior Angles: 3 & 6 ; 4 & 5 Consecutive Interior Angles: 4 & 6 ; 3 & 5

Notes Symbols for parallel in statements and figures The symbol ║ means is parallel to The pink arrows on lines PQ and RS indicate that they are parallel.