Parallel Lines & Transversals

The student is able to (I can):

Identify parallel lines, perpendicular lines, skew lines, and parallel planes

Identify

Transversals

Corresponding angles

Alternate Interior Angles

Alternate Exterior Angles

Same-side Interior Angles

parallel lines

perpendicular lines

Coplanar lines that do not intersect

Two coplanar lines that intersect at right angles (90)

m

nm n

f

gf g

skew lines

parallel planes

Noncoplanar lines that do not intersect

Planes that do not intersect

R

S

Plane R Plane S

transversal A line that intersects two coplanar lines at two different points

r

s

t

corresponding angles

Angles that lie on the same side of the transversal t, on the same sides of lines rand s

Example: 1 and 5

Corresponding angles of parallel lines are congruent.

876

54

312

1 52 63 74 8

t

s

r

alternate interior angles

Angles that lie on opposite sides of the transversal t, between lines r and s

Example: 2 and 7 or 4 and 5

Alternate interior angles of parallel lines are congruent.

r

s

t

interior

87 65

4312 2 7

4 5

alternate exterior angles

Angles that lie on opposite sides of the transversal t, outside lines r and s

Example: 1 and 8

Alternate exterior angles of parallel lines are congruent.

r

s

t

exterior

exterior

87

65

43

12

1 84 5

same-side interior angles

Angles that lie on the same side of the transversal t, between the lines r and s(sometimes called consecutive angles).

Example: 3 and 5

Same-side interior angles of parallel lines are supplementary.

r

s

t

interior

8765

431 2

m3 + m5 = 180m4 + m6 = 180

1. Find the measures of the numbered angles

m1 = 125; m2 = 55;

m3 = 55; m4 = 125;

m5 = 55; m6 = 55;

m7 = 125

2. List each angle pair

corresponding angles

1 & 4; 2 & 5;

3 & 6; 8 & 7

alt. interior angles

3 & 5; 8 & 4

alt. exterior angles

1 & 7; 2 & 6

same-side interior angles

3 & 4; 8 & 5

1 2

3 125(8)

4 56 7

Practice