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

Angles Formed By Parallel Lines Geometry Notes

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

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

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

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

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

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

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

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

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

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

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

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

Homework Lesson 3-2 p.136 #14-38 all 25 problems