Lesson 3-5 Proving Lines Parallel

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Lesson 3-5 Proving Lines Parallel
• Postulate 3.4- If two lines are cut by a
transversal so that the corresponding angles
are congruent, then the lines are parallel.
Example:
• Postulate 3.5- Parallel Postulate
If a given line and a point not on the line, then
there exists exactly one line through the point
that is parallel to the given line.
Proving Lines Parallel
Theorems
3.5 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
3.6 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.
3.7 If two lines in a plane are cut by a transversal so that a
pair of alternate interior angles is congruent, then the lines
are parallel
3.8 In a plane, if two lines are perpendicular to the same
line, then they are parallel
Examples
Determine which lines,
if any, are parallel.
supplementary. So,
consecutive interior angles are
consecutive interior angles are not
supplementary. So, c is not parallel to a or b.
Answer:
Determine which lines, if any, are parallel.
Answer:
ALGEBRA Find x and mZYN so that
Explore From the figure, you know that
and
You also know that
are alternate exterior angles.
Plan For line PQ to be parallel to MN, the alternate exterior
angles must be congruent.
Substitute the given angle measures into this equation
and solve for x. Once you know the value of x, use
substitution to find
Solve
Alternate exterior angles
Substitution
Subtract 7x from each side.
Add 25 to each side.
Divide each side by 4.
Original equation
Simplify.
Examine Verify the angle measure by using the value of x to
find
Since
Answer:
ALGEBRA Find x and mGBA so that
Answer:
Given:
Prove:
Proof:
Statements
1.
2.
3.
4.
5.
6.
7.
.
.
Reasons
1. Given
2. Consecutive Interior Thm.
3. Def. of suppl. s
4. Def. of congruent s
5. Substitution
6. Def. of suppl. s
7. If cons. int. s are suppl.,
then lines are .
Given:
Prove:
Proof:
Statements
Reasons
1.
1. Given
2.
2. Alternate Interior Angles
3.
3. Substitution
4.
.
4. Definition of suppl. s
5.
5. Definition of suppl. s
6.
6. Substitution
7.
7. If cons. int. s are suppl.,
then lines are .
Answer:
Answer: Since the slopes are not equal, r is not parallel to s.

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