Sections 3.2 and 3.3

Parallel Lines & Transversals

GeometryMr. Robinson

Fall 2011

Essential Question:

What results can be determined when parallel lines are cut by a transversal?

Postulate 15 Corresponding s Post.

• If 2 lines are cut by a transversal, then the pairs of corresponding s are .

• i.e. If l m, then 12.

l

m

1

2

Section 3.2 Theorems• Theorem 3.1 – If two lines intersect to

form a linear pair of congruent angles, then the lines are perpendicular.

Section 3.2 Theorems• Theorem 3.2 – If two sides of two adjacent

acute angles are perpendicular, then the angles are complementary.

Section 3.2 Theorems• Theorem 3.3 – If two lines are

perpendicular, then they intersect to form four right angles.

Theorem 3.4Alternate Interior s Theorem

• If 2 lines are cut by a transversal, then the pairs of alternate interior s are .

• i.e. If l m, then 12.

l

m

1

2

Theorem 3.5 Consecutive Interior s Theorem

• If 2 lines are cut by a transversal, then the pairs of consecutive int. s are supplementary.

• i.e. If l m, then 1 & 2 are supp.

l

m 1

2

Theorem 3.6 Alternate Exterior s Theorem

• If 2 lines are cut by a transversal, then the pairs of alternate exterior s are .

• i.e. If l m, then 12.

l m

1

2

• If a transversal is to one of 2 lines, then it is to the other.

• i.e. If l m, & t l, then t m.** 1 & 2 added for proof purposes.

1

2

Theorem 3.7 Transversal Theorem

l

m

t

Ex: Find:

m1=

m2=

m3=

m4=

m5=

m6=

x=

125o 21

3

4 6

5

x+15o

Ex: Find:

m1=55°

m2=125°

m3=55°

m4=125°

m5=55°

m6=125°

x=40°

125o 21

3

4 6

5

x+15o

Assignment

• Pp. 138 – 139 #3-16

• pp. 146 -147 #1-26