geometry section 3-5 1112

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?


Postulates & Theorems1. Converse of Corresponding Angles Postulate


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.


Postulates & Theorems2. Parallel Postulate


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.


Postulates & Theorems3. Alternate Exterior Angles Converse


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.


Postulates & Theorems4. Consecutive Interior Angles Converse


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.


Postulates & Theorems5. Alternate Interior Angles Converse


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.


Postulates & Theorems6. Perpendicular Transversal Converse


Postulates & Theorems6. Perpendicular Transversal Converse

In a plane, if two lines are perpendicular to the same line, then they are parallel.


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. ∠1≅ ∠3

a b since these congruent angles are also corresponding, the Corresponding Angles Converse holds




b. m∠1=103° and m∠4 =100° ∠1 and ∠4




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


Example 2 Find m∠ZYN so that PQ MN.



11x − 25 = 7x + 35



11x − 25 = 7x + 35

4x = 60



11x − 25 = 7x + 35

4x = 60

x =15



11x − 25 = 7x + 35

4x = 60

x =15

m∠ZYN = 7(15) + 35



11x − 25 = 7x + 35

4x = 60

x =15

m∠ZYN = 7(15) + 35 =105 + 35



11x − 25 = 7x + 35

4x = 60

x =15

m∠ZYN = 7(15) + 35 =105 + 35 =140



11x − 25 = 7x + 35

4x = 60

x =15

m∠ZYN = 7(15) + 35 =105 + 35 =140

m∠ZYN =140°


Check Your Understanding

Review problems #1-7 on page 208


Problem Set


Problem Set

p. 209 #9-27 odd, 37

“Nothing in life is to be feared. It is only to be understood.” - Marie Curie


geometry section 3-5 1112

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