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Aim:

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Aim:

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How do we prove lines are parallel?

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Do Now:

1) Name 4 pairs of corresponding angles.

2) Name 2 pairs of alternate interior angles.

3) Name 2 pairs of alternate exterior angles.

4) If lines l and k are extended and they never intersect, what can we say about l and k ?

l || k

5) If lines l and k are extended and they do intersect, what can we say about l and k ?

l is not || k

Geometry Lesson:

Def: Parallel lines have no points in common or have all points in common.

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A

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C

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Line m is “transverse” to lines l and k.

m

Def. Parallel:Def: Transversal

Def: A transversal is a line that intersects two other lines in two different points.

Geometry Lesson: Proving Lines are Parallel

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Ex: Transversals/ angle pairsState the type of each angle pair:

alt. interior

corresponding

alt. interior

alt. exterior

alt. interior

alt. interior

Geometry Lesson: Proving Lines are Parallel

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Theorem #11:

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Two lines cut by a transversal are parallel if a pair of corresponding angles are congruent.

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Theorem #12:

Two lines cut by a transversal are parallel if a pair of alternate interior angles are congruent.

Theorem #13:

Two lines cut by a transversal are parallel if a pair of interior angles on the same side of the transversal are supplementary.

Theorem #14:

Two lines perpendicular to the same line are parallel.

Proving lines parallelm

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Geometry Lesson: Proving Lines are Parallel

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2)

3)

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132

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Ex: Proving lines parallelOr

Geometry Lesson: Proving Lines are Parallel

Given:

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Prove:

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Ex Proving lines parallel:Given

Given

Def. angle bisector

Transitive Postulate

Geometry Lesson: Proving Lines are Parallel

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3) Given:

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Prove:

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Proving lines parallel:1) Given:

Prove:

2) Given:

Prove:

Geometry Lesson: Proving Lines are Parallel