1. 3.3 Parallel Lines & Transversals

2. Standards/Objectives:
Standard 3: Students will learn and apply geometric concepts.
Objectives:
Prove and use results about parallel lines and transversals.
Use properties of parallel lines to solve real-life problems, such as estimating the Earth’s circumference

3. Homework
Pgs #1-30
REMINDER: There is a quiz after If you want a glance at what it kind of looks like, check out pg You will be doing this for homework next class meeting.

4. Postulate 15 Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 1 2
1 ≅ 2

5. Theorem 3.4 Alternate Interior Angles
If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. 3 4
3 ≅ 4

6. Theorem 3.5 Consecutive Interior Angles
If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. 5 6
5 + 6 = 180°

7. Theorem 3.6 Alternate Exterior Angles
If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. 7 8
7 ≅ 8

8. Theorem 3.7 Perpendicular Transversal
If a transversal is perpendicular to one of the two parallel lines, then it is perpendicular to the other. j h k
j  k

9. Example 1: Proving the Alternate Interior Angles Theorem
Given: p ║ q
Prove: 1 ≅ 2 1 2 3

10. Proof Statements: p ║ q 1 ≅ 3 3 ≅ 2 1 ≅ 2 Reasons: Given
Corresponding Angles Postulate
Vertical Angles Theorem
Transitive Property of Congruence

11. Example 2: Using properties of parallel lines
Given that m 5 = 65°, find each measure. Tell which postulate or theorem you use.
A. m 6 B. m 7
C. m 8 D. m 9 9 6 8 5 7

12. Solutions: m 6 = m 5 = 65° m 7 = 180° - m 5 =115°
Vertical Angles Theorem
m 7 = 180° - m 5 =115°
Linear Pair postulate
m 8 = m 5 = 65°
Corresponding Angles Postulate
m 9 = m 7 = 115°
Alternate Exterior Angles Theorem

13. Ex. 3—Classifying Leaves
BOTANY—Some plants are classified by the arrangement of the veins in their leaves. In the diagram below, j ║ k. What is m 1? k j 1
120°

14. Solution
m  ° = 180°
m 1 = 60°
Consecutive Interior angles Theorem
Subtraction POE

15. Ex. 4: Using properties of parallel lines
Use the properties of parallel lines to find the value of x.
125° 4
(x + 15)°

16. Proof Statements: m4 = 125° m4 +(x+15)°=180° 125°+(x+15)°= 180°
Reasons:
Corresponding Angles Postulate
Linear Pair Postulate
Substitution POE
Subtraction POE

17. NOTE:
You must show all your work. Check your syllabus it tells you everything I expect. We are moving into the next quarter shortly, and I expect that your work will be even more professional, neat, organized, and will show even at a casual glance that you did your homework. IF IT EVEN LOOKS COPIED NO CREDIT!!!!