Properties of Parallel Lines

Objectives:

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

parallel linestwo or more co-planar lines

that do not intersect

Co-planar lie on same plane

m//n // 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 lines a & b.

Is line r a transversal?

Yes - it intersects 3 lines.

When parallel lines are cut by a transversal, these special

relationships are formed among the angles!

corresponding angles – CA two angles on the same side

of transversal and on the same side of the parallel lines

Corresponding Angle Conjecture:

If two parallel lines are cut by a transversal, then C.A.’s are

congruent

alternate interior angles – AIA angles that are on opposite

sides of transversal and between the parallel lines

Alternate Interior Angle Conjecture:

If two parallel lines are cut by a transversal, then A.I.A.’s are

congruent.

alternate exterior angles – AEA

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

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 the unknown

< measures.

Measure of < 1 = ?

Measure of < 2 =?

Measure of < 3 =?

Measure of < 4 =?

Measure of < 5 =?

Measure of < 6 =?

Measure of < 7=?

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

If AIA are congruent then are lines m and n parallel??