Parallel Lines & Angle Relationships

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Presentation transcript:

Parallel Lines & Angle Relationships Unit Essential Question: How do parallel and intersecting lines impact angle relationships? Parallel Lines & Angle Relationships

Properties of Parallel Lines Essential Question: What are the angle relationships created by lines cut by a transversal?

Transversal & Angles

Identify the following: Transversal Same-Side Interior Corresponding Angles Alternate Exterior Alternate Interior Same-Side Exterior

What happens when Lines are Parallel?

Corresponding Angles Postulate Do we all AGREE?

Can you Prove these? Use the Corresponding Angles Postulate to prove the following:

Two-Column Proof If P , then Q .

Proof of Alternate Interior Angles

More Theorems

If a Transversal Intersects Two Parallel Lines, then… Corresponding Angles are Congruent Alternate Interior Angles are Congruent Same-Side Interior Angles are Supplementary Alternate Exterior Angles are Congruent Same-Side Exterior Angles are Supplementary

Finding Angle Measures

Finding Angle Measures Find x and y.

Opening Thoughts:

Proving Lines Parallel How do you Prove that Lines are Parallel?

Converse of Corresponding Angles Do you believe it to be true? Can you find any Counterexamples?

Parallel & Perpendicular Lines Essential Question: What are the relationships between parallel and perpendicular lines?

Triangle Angle Sum Essential Question: How do you use Parallel Lines to show that a Triangle has 180 degrees?