Presentation on theme: "3.3 Parallel Lines & Transversals"— Presentation transcript:
1 3.3 Parallel Lines & Transversals
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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
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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 ≅
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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: m4 = 125° m4 +(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!!!!