1. 3-2 Angles and Parallel Lines page 180

2. 1 2 1 2 PROPERTIES OF PARALLEL LINES POSTULATE
POSTULATE 15 Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 1 2

3. 3 4 3 4 PROPERTIES OF PARALLEL LINES THEOREMS ABOUT PARALLEL LINES
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

4. 5 6 m 5 + m 6 = 180° PROPERTIES OF PARALLEL LINES
THEOREMS ABOUT PARALLEL LINES
THEOREM 3.5 Consecutive Interior Angles
If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.
m m 6 = 180° 5 6

5. 7 8 7 8 PROPERTIES OF PARALLEL LINES THEOREMS ABOUT PARALLEL LINES
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

6. j k PROPERTIES OF PARALLEL LINES THEOREMS ABOUT PARALLEL LINES
THEOREM 3.7 Perpendicular Transversal
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.
j k

7. 1  3 Corresponding Angles Postulate
Proving the Alternate Interior Angles Theorem
Prove the Alternate Interior Angles Theorem.
SOLUTION
GIVEN
p || q
PROVE
Statements
Reasons
p || q Given 1
1  Corresponding Angles Postulate 2 3
3  Vertical Angles Theorem
1  Transitive property of Congruence 4

8. which postulate or theorem you use.
Using Properties of Parallel Lines
Given that m = 65°,
find each measure. Tell
which postulate or theorem
you use.
SOLUTION
m = m = 65°
Vertical Angles Theorem
Linear Pair Postulate
m = 180° – m = 115°
Corresponding Angles Postulate
m = m = 65°
Alternate Exterior Angles Theorem
m = m = 115°

9. parallel lines to find the value of x.
PROPERTIES OF SPECIAL PAIRS OF ANGLES
Using Properties of Parallel Lines
Use properties of
parallel lines to find the value of x.
SOLUTION
Corresponding Angles Postulate
m = 125°
Linear Pair Postulate
m (x + 15)° = 180°
Substitute.
125° + (x + 15)° = 180°
Subtract.
x = 40°

10. Ex. 2 Find the values of x, y, and z
MA //HT and NG//EL
2x = 72
X = 36
5y + 2 = 72
5y = 70
Y = 14
4z + 72 = 180
4z = 108
Z = 27 N E M A 4z 2x H T 72
5y+2 G L

11. Given p//q , m<1 =107, and m<11 = 48
Given p//q , m<1 =107, and m<11 = 48. Find the measure of each angle. q p 1 11

12. Find x and y.
4x-5
3y+1
3x+11

13. Find x and y.
Given that a//b, find x and y. a 6y
9x+12
13y-10 b

14. Class work on page 183 problems 1-10
Homework on page 183 problems 11-29