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Presentation on theme: "Click the mouse button or press the Space Bar to display the answers."— Presentation transcript:

1 Click the mouse button or press the Space Bar to display the answers.
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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 c
d

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


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