1. Opener Alternate Interior Angles Alternate Exterior Angles
Same-side Interior Angles
Corresponding Angles

2. Sect. 3.3 Parallel Lines and Transversals.
Goal Properties of Parallel Lines
Goal Properties of Special Pairs of Angles.

3. 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

4. 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

5. 5 6 m 5 + m 6 = 180° Properties of Parallel Lines
THEOREMS ABOUT PARALLEL LINES
THEOREM 3.5 Consecutive (Same-Side) 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

6. 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

7. 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

8. Properties of Parallel Lines
Given that m = 65°,
find each measure. Tell
which postulate or theorem
you use.
SOLUTION
m = m = 65°
Vertical Angles Congruent
Linear Pair Postulate
m = 180° – m = 115°
If lines || corresponding angles 
m = m = 65°
If lines || alternate exterior angles 
m = m = 115°

9. parallel lines to find the value of x.
Properties of Special Pairs of Angles
Use properties of
parallel lines to find the value of x.
SOLUTION
If || corr. s 
m = 125°
If ||, Same-side ext ’s supp.
m (x + 15)° = 180°
Substitute.
125° + (x + 15)° = 180°
Subtract.
x = 40°

10. 80° 100° 80° If EH||GI and EG||HI , find m1 = ___________
Properties of Special Pairs of Angles
If EH||GI and EG||HI , find
m1 = ___________
m2 = ___________
m3 = ___________
80°
100°
80°

11. Solution: x = 116 If the lines are parallel, find the value of x
Properties of Special Pairs of Angles
If the lines are parallel, find the value of x
Solution:
x = 116

12. x + (x - 20) = 2x – 20 because of the AAP.
Properties of Special Pairs of Angles
If the lines are parallel, find the value of x
x + (x - 20) = 2x – 20 because of the AAP.
70° and (2x – 20)° angles are same-side int. angles.
So 70 + (2x – 20) = 180,
Or 2x + 50 = 180.
Solution: x = 65

13. Given: p || q Prove: m1 + m2 = 180°
Properties of Special Pairs of Angles
Given: p || q
Prove: m1 + m2 = 180°

14. 1 m 2 of a circle 50 Properties of Special Pairs of Angles
Estimating Earth’s Circumference: History Connection
Over 2000 years ago Eratosthenes estimated Earth’s circumference by using the fact that the Sun’s rays are parallel.
When the Sun shone exactly down a vertical well in Syene, he measured the angle the Sun’s rays made with a vertical stick in Alexandria. He discovered that
m 2 1 50
of a circle

15. 1 m 2 of a circle 50 m 1 = m 2 1 m 1 of a circle 50
Properties of Special Pairs of Angles
Estimating Earth’s Circumference: History Connection
m 2 1 50
of a circle
Using properties of parallel lines, he knew that
m = m 2
He reasoned that
m 1 1 50
of a circle

16. 1 m 1 of a circle 50 1 of a circle 50 50(575 miles) 29,000 miles
Properties of Special Pairs of Angles
Estimating Earth’s Circumference: History Connection
m 1 1 50
of a circle
The distance from Syene to Alexandria was believed to be 575 miles
Earth’s circumference 1 50
of a circle
575 miles
Earth’s circumference
50(575 miles)
Use cross product property
29,000 miles
How did Eratosthenes know that m = m ?

17. Homework
even, 33-44