Properties of Parallel Lines

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Presentation transcript:

Properties of Parallel Lines Geometry 3-1

Definition Transversal – A line that crosses two other lines Note: the two other lines may be parallel, but do not need to be parallel Definition

Corresponding Angles – Angles that appear in the same relative position X X Definition

Alternate Interior Angles – Angles between the pair of lines and on opposite sides of the transversal X X Definition

Alternate Exterior Angles – Angles outside the pair of lines and on opposite sides of the transversal X X Definition

Same Side Interior Angles – Angles inside the pair of lines and on the same side of the transversal X X Definition

Transversal Same side of Transversal Opposite sides of Transversal Between the Parallel Lines Same Side Interior Alternate Interior Outside the Parallel Lines Alternate Exterior Same position compared to parallel lines Corresponding

X X Corresponding Angles

Consecutive Interior Angles X X

Alternate Interior Angles X X Alternate Interior Angles

X X Corresponding Angles

Alternate Exterior Angles

Consecutive Interior Angles X X Consecutive Interior Angles

Consecutive Interior Angles X X Consecutive Interior Angles

Alternate Interior Angles X X Alternate Interior Angles

Corresponding Angles X X

Alternate Interior Angles X X Alternate Interior Angles

Alternate Exterior Angles

Alternate Exterior Angles

Corresponding Angles X X

Alternate Exterior Angles

Corresponding Angles X X

X X Corresponding Angles

Alternate Interior Angles X X

X X Corresponding Angles

Consecutive Interior Angles X X

X X Corresponding Angles

Alternate Interior Angles X X

Consecutive Interior Angles X X Consecutive Interior Angles

Alternate Exterior Angles

X X Corresponding Angles

Corresponding Angles X X

Investigation

Investigation

Investigation

Conjecture / Postulate If two parallel lines are cut by a transversal, then the corresponding angles are congruent X X Conjecture / Postulate

If two parallel lines are cut by a transversal, then the alternate interior angles are congruent X X Conjecture / Theorem

If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent Conjecture / Theorem

If two parallel lines are cut by a transversal, then the same side interior angles are supplementary X X Conjecture / Theorem

Will these conjectures hold if the lines are not parallel? Try it No Investigation

Practice

Practice

Practice

Practice

Practice

Practice

Pages 119 – 121 10-18, 24, 29 Homework

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