Angle Relationships

Vocabulary Transversal: a line that intersects two or more lines at different points. Transversal: a line that intersects two or more lines at different points.

Exterior Angles: <1, <2, <7, <

34 56 Interior Angles: <3, <4, <5, <6 Interior Angles: <3, <4, <5, <6

34 56 Same-Side Interior Angles: <3 and <5; <4 and <6 Same-Side Interior Angles: <3 and <5; <4 and <6

Same-Side Interior Angle Theorem If two parallel lines are cut by a transversal then each pair of same-side interior angles is supplementary

Converse of the Same-Side Interior Angle Theorem If two lines are cut by a transversal and the same-side interior angles are supplementary, then the lines are parallel. 132º 48º m p l Since = 180, m ║ p

Alternate exterior angles: 1 and 8 2 and 7

Alternate Exterior Angle Theorem If two parallel lines are cut by a transversal, then alternate exterior angles are congruent. Converse of the Alternate Exterior Angle Theorem If two lines are cut by a transversal, and alternate exterior angles are congruent, then the lines are parallel. 75 p q g Since alternate exterior angles are congruent, p ║ q

Alternate interior angles: 3 and 6 4 and 5

Alternate Interior Angle Theorem If two parallel lines are cut by a transversal then each pair of alternate interior angles is congruent. Converse of then Alternate Interior Angle Theorem If two lines are cut by a transversal, and alternate interior angles are congruent, then the lines are parallel.

Corresponding angles: 1 and 52 and 6 3 and 74 and 8 Corresponding angles: 1 and 52 and 6 3 and 74 and

Corresponding Angle Postulate If two parallel lines are cut by a transversal then each pair of corresponding angles are congruent.

Converse of the Corresponding Angle Theorem If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel. e h k 165º Since the corresponding angles are congruent, e ║ h.

In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. Parallel Transversal Theorem If two lines are parallel to the same line, then they are parallel to each other. a b c a ║ b m n p m ║ n

Perpendicular Transversal Theorem In a plane if a line is perpendicular to one of two parallel lines then it is also perpendicular to the other. m n p Since m n and m p, then n p.