2. Parallel Lines & Transversals

3. Alternate Interior Angles
Opposite sides of the transversal & inside the parallels
Are congruent
Equation:
angle = angle

4. Consecutive Interior Angles
Same side of the transversal & inside the parallels
Are supplementary
Equation:
angle + angle = 180

5. Alternate Exterior Angles
Opposite sides of the transversal & outside the parallels
Are congruent
Equation:
angle = angle

6. Corresponding Angles
Same location but at different intersections (only travel on the transversal)
Are congruent
Equation:
angle = angle

7. Identify each angle pair.
1. 1 and 3
2. 3 and 6
3. 4 and 5
4. 6 and 7
corr. s
alt. int. s
alt. ext. s
consec int s

8. Example 1:
Find each angle measure.
A. mECF
x = 70
Corr. s Post.
mECF = 70°
B. mDCE
5x = 4x + 22
Corr. s Post.
x = 22
Subtract 4x from both sides.
mDCE = 5x
= 5(22)
Substitute 22 for x.
= 110°

9. Example 1
Find mQRS.
x = 118
Corr. s Post.
mQRS + x = 180°
Def. of Linear Pair
mQRS = 180° – x
Subtract x from both sides.
= 180° – 118°
Substitute 118° for x.
= 62°

10. Example 2:
Find each angle measure.
A. mEDG
mEDG = 75°
Alt. Ext. s Thm.
B. mBDG
x – 30° = 75°
Alt. Ext. s Thm.
x = 105
Add 30 to both sides.
mBDG = 105°

11. Example 2
Find mABD.
2x + 10° = 3x – 15°
Alt. Int. s Thm.
Subtract 2x and add 15 to both sides.
x = 25
mABD = 2(25) + 10 = 60°
Substitute 25 for x.

12. Example 3:
Find x and y in the diagram.
By the Alternate Interior Angles
Theorem, (5x + 4y)° = 55°.
By the Corresponding Angles Postulate, (5x + 5y)° = 60°.
5x + 5y = 60
–(5x + 4y = 55)
y = 5
Subtract the first equation from the second equation.
Substitute 5 for y in 5x + 5y = 60. Simplify and solve for x.
5x + 5(5) = 60
x = 7, y = 5