3.1.1 Planes, Lines, and Angles Key Objectives • Identify parallel, perpendicular, and skew lines. • Identify the angles formed by two lines and a transversal. Key Terms
• Parallel lines (||) are coplanar and do not intersect. • Perpendicular lines ( ⊥ ) intersect at 90 ° angles. • Skew lines are not coplanar. Skew lines are not parallel and do not intersect. • Parallel planes are planes that do not intersect. • A transversal is a line that intersects two coplanar lines at two different points.
• Corresponding angles lie on the same side of the transversal and on the same side of the other two lines. • Alternate interior angles are nonadjacent angles that lie on opposite sides of the transversal and between the other two lines. • Alternate exterior angles lie on opposite sides of the transversal and outside the other two lines. • Same-side interior angles lie on the same side of the transversal and between the other two lines. Example 1 Classifying Lines and Planes Three classifications of pairs of lines are identified in this example: parallel, perpendicular, and skew lines. Additionally, a pair of planes are also classified as parallel planes.
Perpendicular lines intersect at 90 ° . There are many pairs of perpendicular lines in the given figure, including DH and HG , which can be written symbolically as DH ┴ HG . Additionally, AB ┴ BF , HG ┴ FG , and BC ┴ CD . Skew lines are neither coplanar nor parallel, nor do they intersect. There are many pairs of skew lines in the given figure including AE and DC , as well as HE and CG . Parallel planes do not intersect. Plane ABC is || to plane FGH . Lines are parallel if they are coplanar and do not intersect. The line segments EF and AB are two coplanar lines that do not intersect, so EF || AB . There are many other pairs of parallel lines in the given figure including EF || HG , DH || AE , and BC || AD , to name a few.
131
Made with FlippingBook - Online magazine maker