3.1: Properties of Parallel Lines Every man dies, not every man really lives. -William Wallace Every man dies, not every man really lives.

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Presentation transcript:

3.1: Properties of Parallel Lines Every man dies, not every man really lives. -William Wallace Every man dies, not every man really lives.

Transversal: A line that intersects two coplanar lines at two distinct points. Identifying Angles a b c k l m How many angles are formed by a transversal?

Identifying Angles Alternate Interior Angles: Nonadjacent interior angles that lie on opposite sides of the transversal. Same-Side Interior Angles: Angles that lie on the same side of the transversal between the two lines it intersects Corresponding Angles: Angles that lie on the same side of the transversal in corresponding positions relative to the two lines it intersects

Identifying Angles Alternate Interior Angles: and are alternate interior angles Same-Side Interior Angles: and are same-side interior angles (AKA co-interior angles) Corresponding Angles: and are corresponding angles Also:

Properties of Parallel Lines t 1 l m 2 Postulate 3-1: Corresponding Angles Postulate: If a transversal intersects two parallel lines, then corresponding angles are congruent. Note: Notation for parallel lines

Properties of Parallel Lines Let’s say this angle is 72°… Alternate Interior Angles are congruent!!!

Properties of Parallel Lines Theorem 3-1: Alternate Interior Angles Theorem If a transversal intersects two parallel lines, then alternate interior angles are congruent. a b t 1 32

Proof of Alternate Interior Angles Theorem 1 32 a b t 4 StatementsReasons

Properties of Parallel Lines Same-Side Interior Angles are supplementary!!!

Properties of Parallel Lines Theorem 3-2: Same-Side Interior Angles Theorem If a transversal intersects two parallel lines, then same-side interior angles are supplementary a b t

Identifying Angles Alternate Exterior Angles: Nonadjacent exterior angles that lie on opposite sides of the transversal. Same-Side Exterior Angles: Angles that lie on the same side of the transversal outside of the two lines it intersects

Identifying Angles Alternate Exterior Angles: and are alternate exterior angles Same-Side Exterior Angles: and are same-side exterior angles (AKA co-exterior angles) Also:

Properties of Parallel Lines Alternate Exterior Angles are congruent!!!

Properties of Parallel Lines Theorem 3-3: Alternate Exterior Angles Theorem If a transversal intersects two parallel lines, then alternate exterior angles are congruent. a b 1 3 2

Proof of Alternate Exterior Angles Theorem a b 4 StatementsReasons

Properties of Parallel Lines Same-Side Exterior Angles are supplementary!!!

Properties of Parallel Lines Theorem 3-4: Same-Side Exterior Angles Theorem If a transversal intersects two parallel lines, then same-side exterior angles are supplementary. a b 1 3 2

Let’s Apply What We Have Learned, K? x°y° 50 ° 70 ° Find the values of x and y in the diagram below.

Let’s Apply What We Have Learned, K? x° y° 66 ° 52 ° Find the values of x and y in the diagram below.

3.1: Properties of Parallel Lines Every man dies, not every man really lives. -William Wallace HOMEWORK: 3.1: #5-9, 11-16, TERMS: transversal, alternate interior (exterior) angles, same- side interior (exterior) angles, corresponding angles

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