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Chapter 3: Parallel and Perpendicular Lines. Section 3-1: Properties of Parallel Lines. Objectives. To identify angles formed by two lines and a transversal. To prove and use properties of parallel lines. Vocabulary. Transversal Alternate Interior Angles Same-side Interior Angles
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Chapter 3: Parallel and Perpendicular Lines Section 3-1: Properties of Parallel Lines
Objectives • To identify angles formed by two lines and a transversal. • To prove and use properties of parallel lines.
Vocabulary • Transversal • Alternate Interior Angles • Same-side Interior Angles • Corresponding Angles • Alternate Exterior Angles • Same-side Exterior Angles
Transversal • A transversal is a line that intersects two coplanar lines at two distinct points.
Angle Types • Alternate Interior Angles • Same-side Interior Angles • Corresponding Angles • Alternate Exterior Angles • Same-side Exterior Angles
Postulate 3-1:“Corresponding Angles Postulate” • If a transversal intersects two parallel lines, then corresponding angles are congruent.
Theorem 3-1:“Alternate Interior Angles Theorem” • If a transversal intersects two parallel lines, then alternate interior angles are congruent.
Theorem 3-2:“Same-Side Interior Angles Theorem” • If a transversal intersects two parallel lines, then same-side interior angles are supplementary.
Theorem 3-3:“Alternate Exterior Angles Theorem” • If a transversal intersects two parallel lines, then alternate exterior angles are congruent.
Theorem 3-4:“Same-Side Exterior Angles Theorem” • If a transversal intersects two parallel lines, then same-side exterior angles are supplementary.
Finding Angle Measures • Find the measure of each numbered angle. Justify your answer.
