WARM UP Look through pages Write down the definitions of –Transversals –Interior –Exterior –Alternate Interior Angles –Alternate Exterior Angles –Corresponding Angles

4.5 Parallel lines

Obj: recognize planes, Recognize transversals, identify the pairs of angles formed by a transversal, 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 Plane m m y x

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

Name the alternate interior angles. Name the alternate exterior angles. Name the corresponding angles.

7 m n k When the two lines cut by the transversal are parallel, certain angles are congruent! Given: lines n and m are parallel cut by transversal k

m n k Alternate interior angles are congruent Alternate exterior angles are congruent Corresponding angles are congruent

m n k 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 = 45degrees, name the other angles. m n k

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!