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 1 n 2 3 m 4 5 6 7 8 When the two lines cut by the transversal are parallel, certain angles are congruent!
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!