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Transparency 2

2. Transparency 2a

3. Solving Problems Applying Angle Properties of Lines
Geometry Notes 3-2 & 3-5
Solving Problems Applying Angle Properties of Lines

4. Angles Formed By Parallel Lines
Geometry Notes

5. Star Theorems All vertical angles are congruent
If two parallel lines are cut by a transversal, then:
Corresponding angles are congruent
Alternate interior angles are congruent
Alternate exterior angles are congruent
Same-side interior angles are supplementary

6. Using Theorems to Find Measures of Angles
Given: b ll c Find the measures of each angle. Prove it. m1 = Because… m2 = 2
80o c b a 1

7. Now You Try…
Given: b ll c Find the measure of each angle. Prove it. m3 = Because… m4 = 4 3
63o c b a

8. Example:
Given: a ll d, b ll c Find the measure of each angle. Prove it. m5 = Because… m6 = 5 6
91o d a b c

9. Now You Try…
Given: a ll d, b ll c Find the measures of each angle. Prove it. m7 = Because… m8 = 7 8
59o d a b c

10. Converses of the “Star Theorems”
If corresponding angles are congruent,
then two lines cut by a transversal are
parallel
If alternate interior angles are congruent, then
two lines cut by a transversal are parallel
If alternate exterior angles are congruent, then two lines cut by a transversal are parallel
If same-side interior angles are supplementary,
then two lines cut by a transversal are parallel

11. Examples… Use the diagram to answer the following questions. Prove it.
If 4  6, which two lines must be parallel? Why?
If 11  5, which two lines must be parallel? Why?
If 1 and 8 are supplementary,
which two lines must be parallel? Why?
If 12  5, which two lines
must be parallel? Why? 1 2 3 4 5 6 7 8 9 10 11 12

12. Review
When two parallel lines are cut by a transversal, what angles are congruent?
Alternate interior angles, alternate exterior angles, and corresponding angles
When two parallel lines are cut by a transversal, what angles are supplementary?
Same side interior angles

13. Example Given that a ll b, solve for x. Classify the angles
Determine their relationship 
Set up an equation 
Solve for x.
(10x + 45) b c

14. Now You Try…
Use the same steps as above to solve this problem. Given that k ll l, solve for x p k
(x + 150)
(2x - 15) l

15. Example Given that c ll d and l t, solve for x. l (15x) c (26x + 16) t

16. Now You Try… Given that a ll b, solve for x. (9x-1)۫ 12x ۫ 27x ۫ a b cd

17. Homework
Lesson 3-2 p #14-38 all
25 problems