Review of Parallel Lines Theorems and their Converses.

1. 3.1 Review: Angle Pairs
Corresponding Angles
1 2
∠1 & ∠7 ∠4 & ∠10
4 3
∠3 & ∠5 ∠13 & ∠15 78
9 16
10 15
6 5
Alternate Int. Angles 11 14
∠4 & ∠8 ∠8 & ∠12 12 13
∠3 & ∠7 ∠3 & ∠9
Consecutive Int. Angles
∠2 & ∠9 ∠8 & ∠11
∠3 & ∠8 ∠14 & ∠15
Wednesday, October 13, 2010 1

2. 3.1 Review: Angle Pairs
Alternate Ext. Angles
1 2
∠1 & ∠5 ∠16 & ∠12
4 3
∠2 & ∠6 ∠1 & ∠15 78
9 16
10 15
Same-Side Ext. Angles 6 5
11 14
∠6 & ∠13 ∠5 & ∠2 12 13
∠6 & ∠1 ∠9 & ∠12
Vertical Angles
∠2 & ∠4 ∠11 & ∠13
∠3 & ∠1 ∠9 & ∠15
Wednesday, October 13, 2010 2

3. Solve for the missing angles.
BM 14 and 15
∠1= 127° (linear with 53°)
∠2=53° (vertical with 53°)
∠3=127° (vertical with ∠1)
∠5=53° (corr. with 53°)
∠4=37° (comp. with ∠5)
∠6=90° (vertical with rt. ∠)
∠7=37° (corr. with ∠4)
∠8=143° (linear with ∠7)
∠9=37° (vertical with ∠7)
∠10=143° (vertical with ∠8)
Wednesday, October 13, 2010 3

4. Solve for x and y.
83 + x = 180
(Linear Pair)
x = 97°
83 = y - 13 (alt.
ext. ∠s)
y = 96°
Wednesday, October 13, 2010 4

5. BM 16!!
Prove the Alternate Exterior Angles Theorem
Given: m || l Prove: ∠1 ≅ ∠2
Statements Reasons 1
1. m || l 1. Given 2 3
l
2. ∠1 ≅ ∠3 2. Corr. ∠s are ≅ m
3. ∠3 ≅ ∠2 3. Vertical ∠s are ≅
4. ∠1 ≅ ∠2 4. Transitive
Wednesday, October 13, 2010 5

6. 3.4 Proving Lines are
Parallel
Benchmark 17
Wednesday, October 13, 2010 6

7. What are Proofs?
A “step-by-step” justification
of what you are doing.
Start with the given.
Define what you know.
(Statement, then Reason)
End with your desired
conclusion.
Wednesday, October 13, 2010 7

8. Write the converse:
If t wo lines are parallel, then
their corresponding angles are
congruent.
Corresponding Angles
Converse Postulate
If t wo lines have corresponding
angles congruent, then the lines
are parallel.
Wednesday, October 13, 2010 8

9. Write the converse:
If t wo lines are parallel, then
their alternate interior angles
are congruent.
Alternate Interior Angles
Converse Theorem
If t wo lines have alternate
interior angles congruent, then
the lines are parallel.
Wednesday, October 13, 2010 9

10. Write the converse:
If t wo lines are parallel, then
their consecutive interior
angles are supplementary.
Consecutive Interior Angles
Converse Theorem
If t wo lines have consecutive
interior angles supplementary,
then the lines are parallel.
Wednesday, October 13, 2010 10

11. Is it possible to show lines m and n
are parallel? Why?
Ex. 1:
50° Yes, Alternate
50° Interior Angles
n Converse
Ex. 2: m
80°
Yes, Consecutive
100° Interior Angles
n Converse
Wednesday, October 13, 2010 11

12. What value makes these
lines parallel?
•These angles are
alternate exterior angles 4x + 4°
•If alternate exterior
angles are congruent
(equal), then the lines are
parallel 92°
4x + 4 = 92
4x = 88
x = 22
Wednesday, October 13, 2010 12

13. BM #13: Proving Parallel
Lines c
Given the angle d
relationship, which lines 1
2
4 3
are parallel and why? 78
9
16
10
6 5 15
Ex. 3: ∠1≅∠5 11 14 b
a || b by alt. ext. converse 12 13
a
Ex. 4: ∠8≅∠12
Ex. 5: ∠2 and ∠9 are
c || d by alt. int. converse supplementary
c || d by con. int. converse
Wednesday, October 13, 2010 13

14. Summary:
The Angle Theorems state “If lines
are parallel, then angles are ≅ or
supplementary.”
The Converse Theorems state “If
angles are ≅ or supplementary,
then the lines are parallel.”
Wednesday, October 13, 2010 14

15. Assignment:
#18 3-2 WS p. 295 (Due at
the end of class)
#19 p. 137 ##1-9 (odd),
10-20 (all), 26, 27, 30, 51,
52, 56-62 (even)
Wednesday, October 13, 2010 15