Download Section 3.3 Day 1 Parallel Lines and Transverals

Week 1
Warm Up
10.19.11
State the postulate or theorem:
1)
If ∠ 1 and ∠ 2 are vertical angles, then ∠ 1 ≅ ∠ 2.
2)
If ∠ 1 ≅ ∠ 2 and ∠ 2 ≅ ∠ 3, then ∠ 1 ≅ ∠ 3.
3)
If ∠1 and ∠2 form a linear pair,
then m∠1 + ∠2 = 180º.
Geometry
3.3 Day 1
I will prove and use results about
parallel lines and transversals.
P 15
Corresponding Angles
If two parallel lines are cut by a transversal, then the
pairs of corresponding angles are congruent.
1
2
∠1≅∠2
Theorem
3.4
Alternate Interior Angles
If two parallel lines are cut by a transversal, then
the pairs of alternate interior angles are
congruent.
3
4
∠3≅∠4
Ex 1
Prove: ∠ 1 ≅ ∠ 2
j
1
3
Step
j∥k
k
2
Reason
given
∠1≅∠3
Corresponding Angles
Postulate ( P15 )
∠3≅∠2
Vertical Angles
Theorem
∠1≅∠2
Transitive property of Equality
Theorem
3.5
Consecutive Interior Angles
If two parallel lines are cut by a transversal, then
the pairs of consecutive interior angles are
supplementary.
5
6
∠ 5 + ∠ 6 = 180º
Theorem
3.6
Alternate Exterior Angles
If two parallel lines are cut by a transversal, then
the pairs of alternate exterior angles are
congruent.
7
8
∠7 ≅∠8
Ex 2
m∠ 5 = 65º
6
7
angle
measure
5
9
8
Postulate or Theorem
m∠ 6
= m∠ 5
= 65º
m∠ 7
= 180 - m∠ 5
= 115º
m∠ 8
= m∠ 5
= 65º
m∠ 9
= m∠ 7
= 115º
Do: 1
What is the measure of ∠ 5?
5
1
Assignment:
m∠ 1 = 45º
Textbook Page 146, 8 - 17 all