# Parallel Lines Transversals Mrs Wedgwood Geometry Parallel Lines

• Slides: 18

Parallel Lines & Transversals Mrs. Wedgwood Geometry

Parallel Lines and Transversals What would you call two lines which do not intersect? _______ Exterior Interior Exterior A solid arrow placed on two lines of a diagram indicate the lines are parallel. The symbol ____ is used to indicate parallel lines. AB ___ CD

Parallel Lines and Transversals A slash through the parallel symbol || indicates the lines are not parallel. ________

Transversal A _______, or segment that intersects 2 or more ______ lines, rays, or segments. Exterior Parallel lines Interior Non-Parallel lines Interior Exterior transversal

Parallel Lines and Transversals Transversal A _____ is a _______ which intersects ____ or _____ lines in a plane. The intersected lines do not have to be parallel. Lines j, k, and m are intersected by line t. Therefore, line t is a ______ of lines j, k, and m.

INTERIOR –The space ______ the 2 lines interior EXTERIOR -The space _____ the 2 lines exterior

Special Angle Relationships ________ Exterior 1 3 4 Interior 5 6 7 8 Exterior 2 <3 & <6 are ____ Interior angles <4 & <5 are ____ Interior angles <3 & <5 are _____ Interior angles <4 & <6 are _____Interior angles Exterior Angles <1 & <8 are Alternate ____ angles <2 & <7 are _____ Exterior angles <1 & <7 are Same Side _______ angles <2 & <8 are ______ Exterior angles

Special Angle Relationships WHEN THE LINES ARE PARALLEL Exterior 1 2 3 4 Interior 5 6 7 8 Exterior If the lines are not parallel, these angle relationships DO NOT EXIST. ♥Alternate Interior Angles are _______ ♥Alternate Exterior Angles are ________ ♥Same Side Interior Angles are ________ ♥Same Side Exterior Angles are _________

Corresponding Angles & Consecutive Angles Corresponding Angles: Two ____ that occupy _______ positions. _________, ______ Exterior 1 3 4 5 7 2 6 8 Interior Exterior

Corresponding Angles When two parallel lines are cut by a transversal, pairs of corresponding angles are formed. L Line L _______ G P A D B Q E F Line M Line N _____________of corresponding angles are formed. Corresponding pairs of angles are ________.

Same Side Interior/Exterior Angles Same Side Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal. m 3 +m 5 = 180º, m 4 +m 6 = 180º Same Side Exterior Angles: Two angles that lie outside parallel lines on the same sides of the transversal. Exterior 1 2 m 1 +m 7 = 180º, m 2 +m 8 = 180º 3 4 Interior 5 6 7 8 Exterior

Interior Angles The angles that lie in the area between the two parallel lines that are cut by a transversal, are called interior angles. L G Line L Exterior A 1200 P 1200 600 D B 600 F ________ Line N _________ Interior E Q Line M Exterior A pair of interior angles lie on the ______of the transversal.

Alternate Interior/Exterior Angles • _________: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair). ____________________: Two angles that lie outside parallel lines on opposite sides of the transversal. _________ 1 2 Exterior 3 4 Interior 5 7 6 8 Exterior

Alternate Interior Angles Alternate angles are formed on opposite sides of the transversal and at different intersecting points. L A D G Line L P B Q E Line M Line N ____________ F ______of alternate angles are formed. Pairs of alternate angles are _______.

Let’s Practice 120 1 3 7 4 6 5 8 2 m<1=_____° Find all the remaining angle measures.

Another practice problem 40 120 Find all the missing angle measures, and name the postulate or theorem that gives us permission to make our statements.

Name the pairs of the following angles formed by a transversal.