Properties of Parallel Lines Tutorial 7c

Angles and Intersecting Lines A transversal is a line that intersects two coplanar lines at two distinct points. Line t below is a transversal because it intersects lines l and m 1 2 l 1, 2, 7, and 8 are all considered to be exterior angles. 3 4 3, 4, 5, and 6 are all considered to be interior angles. 5 6 m 7 8 t

Angles and Intersecting Lines Corresponding Angles: A pair of angles that lie on the same side of the transversal yet one lies on the interior and one lies on the exterior. 1 and 5 2 and 6 3 and 7 4 and 8 Alternate Interior angles: A pair of interior angles that lie on alternate sides of the transversal. 3 and 6 4 and 5 Same-side Interior angles: A pair of interior angles that lie on the same side of the transversal. 3 and 5 4 and 6 1 2 l 3 4 Alternate-Exterior angles: A pair of exterior angles that lie on the alternate sides of the transversal. 1 and 8 2 and 7 5 6 m 7 8 t

Parallel Lines Parallel Lines are two or more lines on the same plane(coplaner) that do not intersect. m n m || n Line m is parallel to line n. We can write this using the following symbol

Corresponding Angles Postulate If two parallel lines are cut by a transversal, then corresponding angles are congruent. Corresponding Angles 1  5 2  6 3  7 4  8 l 1 2 4 3 5 6 m 7 8 t

Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then alternate interior angles are congruent. Alternate Interior angles 3  6 4  5 l 1 2 4 3 5 6 m 7 8

Same-Side Interior Angles Theorem If two parallel lines are cut by a transversal, then the pairs of same-side interior angles are supplementary. l 1 2 4 3 5 6 m 7 8

Alternate Exterior Angles Theorem If two parallel lines are cut by a transversal, then alternate exterior angles are congruent. Alternate Exterior angles 1  8 2  7 l 1 2 4 3 5 6 m 7 8

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Corresponding Angles Alternate Interior Angles Same-side Interior Angles 4. Alternate Interior Angles Same-side Interior Angles Corresponding Angles

*Double arrows mean that the lines are parallel. Click here to check your answers

*Double arrows mean that the lines are parallel. Same-side Interior Angles x + 121 = 180 x = 59 Same-side Interior Angles x + 117 = 180 x = 63 Same-side Interior Angles x + 74 = 180 x = 106 Same-side Interior Angles x + 68 = 180 x = 112 Same-side Interior Angles x + 109 = 180 x = 71 Same-side Interior Angles x + 90 = 180 x = 90

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m1 = 60º Alternate Interior Angles: Alternate Interior Angles: m1 = 130º Alternate Interior Angles: m1 = 40º

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