1. Angles Formed by Parallel Lines and Transversals 3-2
Warm Up
Lesson Presentation
Lesson Quiz
Holt Geometry

2. Warm Up
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
same-side int s

3. Objective
Prove and use theorems about the angles formed by parallel lines and a transversal.

4. What is the difference between the two figures?
These lines appear to be parallel

5. What do you notice about the corresponding angles in both figures?
Figure A
Figure B
What do you notice about the corresponding angles in both figures?
In figure B, one angle looks like it is obtuse and the other is acute-y
In figure A, the angles look like they are the same measure

6. When a transversal slashes two PARALLEL lines, things start getting fun!

7. What kind of angles are 1 and 3?
Reminder: we are strictly talking parallel lines here… 1 3
What do you think is the relationship between these two angles?
What kind of angles are 1 and 3?
Corresponding
They’re congruent!

8. Reminder: we are strictly talking parallel lines here…
So… the Corresponding Angles Postulate is that if two parallel lines are cut by a transversal, then ALL of the pairs of corresponding angles are congruent... Wow!

9. What is the relationship between alternate exterior angles?
Reminder: we are strictly talking parallel lines here…
What is the relationship between alternate exterior angles?
They’re congruent

10. What is the relationship between alternate interior angles?
Reminder: we are strictly talking parallel lines here…
What is the relationship between alternate interior angles?
They’re congruent

11. What is the relationship between consecutive interior angles?
Reminder: we are strictly talking parallel lines here…
What is the relationship between consecutive interior angles?
They’re supplementary

12. Example 1: Using the Corresponding Angles Postulate
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°

13. Check It Out! 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°

14. If a transversal is perpendicular to two parallel lines, all eight angles are congruent. (all 90 degrees)
Let’s think…

15. Example 2: Finding Angle Measures
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°

16. Check It Out! 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.

17. Example 3: Music Application
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

18. Check It Out! Example 3
Find the measures of the acute angles in the diagram.
By the Alternate Exterior Angles
Theorem, (25x + 5y)° = 125°.
By the Corresponding Angles Postulate, (25x + 4y)° = 120°.
An acute angle will be 180° – 125°, or 55°.
The other acute angle will be 180° – 120°, or 60°.

19. Lesson Quiz
State the theorem or postulate that is related to the measures of the angles in each pair. Then find the unknown angle measures.
1. m1 = 120°, m2 = (60x)°
2. m2 = (75x – 30)°,
m3 = (30x + 60)°
Alt. Ext. s Thm.; m2 = 120°
Corr. s Post.; m2 = 120°, m3 = 120°
3. m3 = (50x + 20)°, m4= (100x – 80)°
4. m3 = (45x + 30)°, m5 = (25x + 10)°
Alt. Int. s Thm.; m3 = 120°, m4 =120°
Same-Side Int. s Thm.; m3 = 120°, m5 =60°