Download Proving Lines Parallel

Proving Lines Parallel
Proving Lines Parallel
•Determine the relationships between
angle pairs formed by a transversal.
•Use these relationships to prove two
lines are parallel.
•Language Objectives:
• Explain the supplementary and
congruent natures of the angle pairs
iff
•If two things equal the same thing,
then they are equal to each other.
iff
•If two things equal the same thing,
then they are equal to each other.
•Two things equal the same thing
⇒ they are equal
iff
•If two things equal the same thing,
then they are equal to each other.
•Two things equal the same thing
⇒ they are equal
•If two things equal each other,
then they equal the same thing.
iff
•If two things equal the same thing,
then they are equal to each other.
•Two things equal the same thing ⇒
they are equal
•If two things equal each other, then
they equal the same thing.
•Two things are equal ⇒ they equal
the same thing
Iff
•Since that sentence works in both
directions, we say:
•Iff two things equal the same
thing, then they equal each other.
•Two things equal the same thing
⇔ they equal each other.
Iff
•If angles are vertical, then they
are congruent.
Iff
•If angles are vertical, then they
are congruent.
•Angle are vertical ⇒ they are
congruent
Iff
•If angles are vertical, then they
are congruent.
•Angle are vertical ⇒ they are
congruent
•If angles are congruent, then they
are vertical.
Iff
•If angles are vertical, then they are
congruent.
•Angle are vertical ⇒ they are
congruent
•If angles are congruent, then they
are vertical.
•Angles are congruent ⇏ they are
vertical.
Notecards
•Vertical Angles are always
congruent.
•If an angle or segment is bisected,
both sides are congruent.
Relationships
Notecards
•Corresponding Angles: Iff two
lines are parallel, the corresponding
angles of the transversal are
congruent.
Notecards
•Alternate Interior Angles: Iff two
lines are parallel, the alternate
interior angles of the transversal
are congruent.
Notecards
•Alternate Exterior Angles: Iff
two lines are parallel, the alternate
exterior angles of the transversal
are congruent.
Notecards
•Consecutive Interior Angles: Iff
two lines are parallel, the
consecutive interior angles of the
transversal are supplementary.
Example 1
•Solve for 𝑥 and 𝑦:
Examples 2 and 3
•Solve for 𝑥 and 𝑦.
Examples 3 and 4
•Solve for 𝑥.
Example 5
Example 6
Example 7
Example 8
Example 9
•Are these lines parallel? Prove why
or why not.
Example 10
•Are these lines parallel? Prove why
or why not.