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3-1 Parallel and Perpendicular Lines 3-1 Parallel Lines and Transversals • Identify the relationships between two lines and planes. • Parallel lines – Two or more lines that are coplanar and do not intersect. • Parallel planes – Two or more planes that do not intersect. • Skew – Two lines that do not intersect and are not coplanar. 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. 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 give line. Identifying Angles formed by Transversals • Transversal – A line that intersects two or more coplanar lines at different points. t • Interior angles • <1, <2, <3, <4 • Exterior angles • <5, <6, <7, <8 Corresponding Angles • Angles on the same side of the transversal. • One angle is an interior angle and the other is an exterior angle • They are not adjacent • <1 and <5 • <2 and <6 • <3 and <7 1 2 • <4 and <8 3 4 5 7 8 6 Alternate Interior Angles • Two interior angles that lie between the two lines on opposite sides of the transversal. • <4 and <5 • <3 and <6 1 2 3 4 5 7 8 6 Alternate Exterior Angles • Two exterior angles that lie outside the two lines on opposite sides of the transversal. • <1 and <8 • <2 and <7 1 2 3 4 5 7 8 6 Consecutive Interior Angles • Two angles that lie between the two lines on the same side of the transversal. • <3 and <5 • <4 and <6 1 2 3 4 5 7 8 6 • Consecutive interior angles are sometimes called same side interior angles. • Name all planes parallel ABC. • Name all segments that • Name all segments that to HB. • Name all segments that FH. • Name all segments • Perpendicular to FC. to plane intersect AB are parallel are skew to • Vertical angles • Supplementary angles • Exterior angles • Interior angles • Consecutive interior angles • Alternate interior angles • Alternate exterior angles • Corresponding angles t m 1 2 4 3 6 8 5 7 l Assignments • Class work page 175 problems 1-20 • Homework page 176 problems 21-36