Properties of Parallel Lines

Objectives:Explore relationships of the angles of parallel lines cut by a transversal.

parallel l ines - two or more co-planar lines that do not intersect

Co-planar - lie on same plane

mn o

No - they intersect (cross).

Are these two lines parallel?

No - they will intersect if you extend the lines.

Are these two lines parallel?

It sure looks like they are!

Are these two lines parallel?

transversal - a line that intersects 2 or more lines

Line n is a transversal. It intersects line a & b.

Is line r a transversal?

Yes - it intersects 3 lines.

corresponding angles - two angles on the same side of transversal and on the same side of the parallel lines

< 1 and 1 5 are corresponding angles. List

the other 3 pairs of corresponding c ’s.

alternate interior angles - angles that are on opposite sides of transversal and between the parallel lines

< 3 and 3 6 are alternate interior angles. List the other pair of A.I.A.’s.

4 & 5

alternate exterior angles - angles that are on opposite sides of transversal and not between the parallel lines

< 1 and 1 8 are alternate exterior angles. List the other pair of A.E.A.’s.

2 & 7

When parallel lines are cut by a transversal, there are special relationships among the angles formed…..let’s investigate!

Compare the measures of pairs of corresponding angles…what do you see? C-17a Corresponding

Angle Conjecture:If two parallel lines are cut by a transversal, then C.A.’s are ___________. congruent

Compare the measures of pairs of alternate interior angles…what do you see? C-17b Alternate Interior

Angle Conjecture:If two parallel lines are cut by a transversal, then A.I.A.’s are ___________. congruent

Compare the measures of pairs of alternate exterior angles…what do you see? C-17c Alternate Exterior

Angle Conjecture:If two parallel lines are cut by a transversal, then A.E.A.’s are ___________. congruent

Sketch this diagram. Write in unknown angle measures.

Measure of M 1 =?

Measure of M 1 =?

Measure of M 2 =?

Measure of M 2 =?

Measure of M 3 =?

Measure of ∠ 3 =?

Measure of M 4 =?

Measure of M 4 =?

Measure of M 5 =?

Measure of M 5 =?

Measure of M 6 =?

Measure of M 6 =?

Measure of M 7=?

Measure of M 7=?

You just found 7 angle measures when you were given only one angle measure!

You know that if two lines are parallel, then the transversal will form congruent alternate interior angles.

Do you think line m is parallel to line n? Why?