WARM UP Look through pages 192-195 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

12

34

56

78

Name the alternate interior angles.

Name the alternate exterior angles.

Name the corresponding angles.

7m

n

k

1 23 4

5 68

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

1 23 4

5 68

Alternate interior angles are congruent

Alternate exterior angles are congruent

Corresponding angles are congruent

m

n

k

1 23 4

5 68

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

1 23 4

5 68

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!