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3.2 use parallel lines and transversals

parallel, transversal, geometry, theorem, exterior angles, interior, corresponding, alternate

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3.2 use parallel lines and transversals

1. 1. 3.2 Use Parallel lines and3.2 Use Parallel lines and TransversalsTransversals Mr. Saucedo Geometry Milby High School
2. 2. OBJECTIVE:OBJECTIVE: We will pair angle theorems to find measurements of angles.
3. 3. ACTIVITYACTIVITY Materials: ◦ Activity worksheet ◦ Protractor Step 1: Measure all the angles created by the transverals in the pictures. Step 2: Look for patterns. Step 3: Explain your patterns.
4. 4. POSTULATE 15:POSTULATE 15: CORRESPONDING ANGLESCORRESPONDING ANGLES If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.
5. 5. THEOREM 3.1:THEOREM 3.1: Alternate Interior Angles TheoremAlternate Interior Angles Theorem If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. <1 ≈ <2 m<1 = m<2
6. 6. THEOREM 3.2:THEOREM 3.2: Alternate Exterior Angles TheoremAlternate Exterior Angles Theorem If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. <1 ≈ <8 m<1 = m<2
7. 7. THEOREM 3.3:THEOREM 3.3: Consecutive Interior AnglesConsecutive Interior Angles TheoremTheoremIf two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. m<3 + m<5 = 180 or m<4 + m<6 = 180
8. 8. CHECKPOINTCHECKPOINT TRUE OR FALSE? 1. Angles A and H are congruent. 2. Angles C and E add up to 180 degrees. 3. Angles D and F add up to 180 degrees. 4. Angles B and G are congruent. 5. Angles A and G add up to 180 degrees. 6. Angles D and E add up to 180 degrees. 7. Angles D and F are supplementary.
9. 9. CHECKPOINTCHECKPOINT True or False? 1.Angles 4 and 6 are congruent. 2.Angles 2 and 5 are congruent. 3.Angles 7 and 1 add up to 180 degrees. 4.Angles 3 and 8 are congruent. 5.Angles 8 and 2 add up to 180 degrees.
10. 10. GUIDEDGUIDED PROBLEMPROBLEM If m<1 = 30, find the Measurement of all the Other angles. 1 = 5= 2= 6= 3= 7= 4= 8=
11. 11. GUIDED PROBLEMGUIDED PROBLEM m<f = 115 and m<c = x + 5, Find x.
12. 12. CHECKPOINTCHECKPOINT m<d = 135 and m<f = x – 30. Find x.
13. 13. INDEPENDENT PRACTICEINDEPENDENT PRACTICE BIG BOOK: PAGE 157 PROBLEMS: 1, 4, 5, 6, 7, 8, 10, 12, 14, 18, 22, 33. PRE-AP: ADD PROBLEM 28.
14. 14. HOMEWORK:HOMEWORK: SECTION 3.2 WORKBOOK, PAGE 46 & 47 PROBLEMS: 1-20 all problems.