Section 3-5Proving Lines Parallel
Wednesday, January 4, 2012
Essential Questions
• How do you recognize angle pairs tha occur with parallel lines?
• How do you prove that two lines are parallel using angle relationships?
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Postulates & Theorems1. Converse of Corresponding Angles Postulate
Wednesday, January 4, 2012
Postulates & Theorems1. Converse of Corresponding Angles Postulate
If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are
parallel.
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Postulates & Theorems2. Parallel Postulate
Wednesday, January 4, 2012
Postulates & Theorems2. Parallel Postulate
If given a line and a point not on the line, then there exists exactly one line through the point that is parallel
to the given line.
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Postulates & Theorems3. Alternate Exterior Angles Converse
Wednesday, January 4, 2012
Postulates & Theorems3. Alternate Exterior Angles Converse
If two lines in a plane are cut by a transversal so that a pair of alternate exterior angles is congruent, then the
two lines are parallel.
Wednesday, January 4, 2012
Postulates & Theorems4. Consecutive Interior Angles Converse
Wednesday, January 4, 2012
Postulates & Theorems4. Consecutive Interior Angles Converse
If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary,
then the lines are parallel.
Wednesday, January 4, 2012
Postulates & Theorems5. Alternate Interior Angles Converse
Wednesday, January 4, 2012
Postulates & Theorems5. Alternate Interior Angles Converse
If two lines in a plane are cut by a transversal so that a pair of alternate interior angles is congruent, then the
two lines are parallel.
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Postulates & Theorems6. Perpendicular Transversal Converse
Wednesday, January 4, 2012
Postulates & Theorems6. Perpendicular Transversal Converse
In a plane, if two lines are perpendicular to the same line, then they are parallel.
Wednesday, January 4, 2012
Example 1Given the following information, is it possible to prove that any of the lines shown are parallel? If so, state the
postulate or theorem that justifies your answer.
a. ∠1≅ ∠3
Wednesday, January 4, 2012
Example 1Given the following information, is it possible to prove that any of the lines shown are parallel? If so, state the
postulate or theorem that justifies your answer.
a. ∠1≅ ∠3
a b since these congruent angles are also corresponding, the Corresponding Angles Converse holds
Wednesday, January 4, 2012
Example 1Given the following information, is it possible to prove that any of the lines shown are parallel? If so, state the
postulate or theorem that justifies your answer.
b. m∠1=103° and m∠4 =100° ∠1 and ∠4
Wednesday, January 4, 2012
Example 1Given the following information, is it possible to prove that any of the lines shown are parallel? If so, state the
postulate or theorem that justifies your answer.
b. m∠1=103° and m∠4 =100° ∠1 and ∠4 are alternate interior angles, but not congruent, so a is not parallel to c
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Example 2 Find m∠ZYN so that PQ MN.
Wednesday, January 4, 2012
Example 2 Find m∠ZYN so that PQ MN.
11x − 25 = 7x + 35
Wednesday, January 4, 2012
Example 2 Find m∠ZYN so that PQ MN.
11x − 25 = 7x + 35
4x = 60
Wednesday, January 4, 2012
Example 2 Find m∠ZYN so that PQ MN.
11x − 25 = 7x + 35
4x = 60
x =15
Wednesday, January 4, 2012
Example 2 Find m∠ZYN so that PQ MN.
11x − 25 = 7x + 35
4x = 60
x =15
m∠ZYN = 7(15) + 35
Wednesday, January 4, 2012
Example 2 Find m∠ZYN so that PQ MN.
11x − 25 = 7x + 35
4x = 60
x =15
m∠ZYN = 7(15) + 35 =105 + 35
Wednesday, January 4, 2012
Example 2 Find m∠ZYN so that PQ MN.
11x − 25 = 7x + 35
4x = 60
x =15
m∠ZYN = 7(15) + 35 =105 + 35 =140
Wednesday, January 4, 2012
Example 2 Find m∠ZYN so that PQ MN.
11x − 25 = 7x + 35
4x = 60
x =15
m∠ZYN = 7(15) + 35 =105 + 35 =140
m∠ZYN =140°
Wednesday, January 4, 2012
Check Your Understanding
Review problems #1-7 on page 208
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Problem Set
Wednesday, January 4, 2012
Problem Set
p. 209 #9-27 odd, 37
“Nothing in life is to be feared. It is only to be understood.” - Marie Curie
Wednesday, January 4, 2012