Parallel Lines Lesson 4.5 Objective: Recognize planes and transversals, identify the pairs of angles formed by a transversal and recognize parallel lines. Plane: •A surface with any two points connected by a line. There must be at least one point not on the line. •Has only two dimensions, length and width (infinite). •Has no thickness. y x Plane m m Coplanar: • Points that lie on the same plane (like collinear). Non-coplanar: • Points that do not lie on the same plane. Transversals: • A line that intersects two coplanar lines in two distinct points. Not always parallel. Parts of a transversal: Exterior region Interior region Exterior region Transversals angles: • Alternate Interior Angles: angles on opposite sides of the transversal in the interior region. • Alternate Exterior Angles: angles on opposite sides if the transversal in the exterior region. • Corresponding Angles: angles in the same position in relation to the transversal. 1 5 2 6 3 7 4 8 Name the alternate interior angles. 2 & 7 6 & 3 Name the alternate exterior angles. 1 & 8 5 & 4 Name the corresponding angles. 1 & 3, 2 & 4, 5 & 7, 6 & 8 Given: lines n and m are parallel cut by transversal k k n m 1 2 3 4 5 6 7 When the two lines cut by the transversal are parallel, certain angles are congruent! 8 k n m 1 2 3 4 5 6 7 8 Alternate interior angles are congruent. Alternate exterior angles are congruent. Corresponding angles are congruent. k n m 1 2 3 4 5 6 7 8 Name the alternate interior angles. Name the alternate exterior angles. Name the corresponding angles. What other angles are congruent??? Notice: if you know one angle in a set of transversal lines where two of the lines are parallel, you know all eight angles. Given: <1 = 45°name the other angles. k n m 1 2 3 4 5 6 7 8 Parallel lines: • Two coplanar lines that do not intersect. (equidistance apart) • Symbol ll or on lines > > • Segments and rays can also be parallel. • To be parallel, the lines MUST BE COPLANAR! Skew lines: • Lines that never touch aren’t coplanar or parallel!
