Properties of Parallel Lines Geometry 3 1 Transversal

• Transversal – A line that crosses two other lines Note: the two

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

• Alternate Interior Angles – Angles between the pair of lines and on

• Alternate Exterior Angles – Angles outside the pair of lines and on

• Same Side Interior Angles – Angles inside the pair of lines and

Transversal Same side of Transversal Between the Parallel Same Side Lines Interior Outside the

• If two parallel lines are cut by a transversal, then the corresponding

• If two parallel lines are cut by a transversal, then the alternate

• If two parallel lines are cut by a transversal, then the same

• Will these conjectures hold if the lines are not parallel? • Try

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

• Pages 119 – 121 • 10 - 24, 29 Honors Homework

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Properties of Parallel Lines Geometry 3 -1

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

X X Corresponding Angles

Consecutive Interior Angles X X

X X Alternate Interior Angles

X X Corresponding Angles

X X Alternate Exterior Angles

X X Consecutive Interior Angles

X X Alternate Interior Angles

Corresponding Angles X X

X X Alternate Interior Angles

X X Alternate Exterior Angles

Corresponding Angles X X

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

X X Consecutive Interior Angles

Alternate Exterior Angles X X

X X Corresponding Angles

Corresponding Angles X X

Investigation

• 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 X X 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

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

• Pages 119 – 121 • 10 - 24, 29 Honors Homework