Properties of Parallel Lines

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 m n o

Are these two lines parallel? No - they intersect (cross). b a

Are these two lines parallel? No - they will intersect if you extend the lines. c d

Are these two lines parallel? It sure looks like they are! e f

transversal – a line that intersects 2 or more lines

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

a c b r 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 – CAtwo angles on the same side of transversal and on the same side of the parallel lines

1 2 4 3 5 6 8 7 Corresponding Angle Conjecture:If two parallel lines are cut by a transversal, then C.A.’s arecongruent

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

1 2 3 4 5 6 7 8 Alternate Interior Angle Conjecture:If two parallel lines are cut by a transversal, then A.I.A.’s are congruent.

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

1 2 3 4 5 6 7 8 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. 2 1 3 4 5 68 6 7

Measure of < 1 = ? 2 1 68 3 4 5 68 6 7

Measure of < 2 =? 2 112 68 3 4 5 68 6 7

Measure of < 3 =? 112 68 3 112 4 5 68 6 7

Measure of < 4 =? 112 68 112 4 68 5 68 6 7

Measure of <5 =? 112 68 112 68 5 112 68 6 7

Measure of < 6 =? 112 68 112 68 112 68 112 6 7

Measure of < 7=? 112 68 112 68 112 68 112 7 68

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?? m 59 59 n

m 59 59 n