3.2 Parallel Lines and Transversals. Geometry 3.2 Parallel Lines and Transversals.

Geometry 3.2 Parallel Lines and Transversals Goals Prove and use results about parallel lines and transversals. Use properties about parallel lines to solve problems. November 2, 2019 Geometry 3.2 Parallel Lines and Transversals

Theorem 3.1: Corr. Angles Theorem. m || n n If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. November 2, 2019 Geometry 3.2 Parallel Lines and Transversals

This means ALL corresponding angles are congruent. 1 2 3 4 5 6 7 8 1  5 2  6 3  7 4  8 November 2, 2019 Geometry 3.2 Parallel Lines and Transversals

Geometry 3.2 Parallel Lines and Transversals Example 120° ? 60° 60° ? 120° ? 120° ? 60° ? 60° ? ? 120° November 2, 2019 Geometry 3.2 Parallel Lines and Transversals

Theorem 3.2 Alt Int ’s Theorem If two parallel lines are cut by a transversal, then alternate interior angles are congruent. 2 lines ||  alt int s  November 2, 2019 Geometry 3.2 Parallel Lines and Transversals

Theorem 3.3 Alt Exterior ’sTheorem If two parallel lines are cut by a transversal, then alternate exterior angles are congruent. 2 lines ||  alt ext s  November 2, 2019 Geometry 3.2 Parallel Lines and Transversals

Theorem 3.4 Same side Int ’s Theorem If two parallel lines are cut by a transversal, then same side interior angles are supplementary. m1 + m2 = 180 m3 + m4 = 180 1 3 2 4 2 lines ||  ss int s supp November 2, 2019 Geometry 3.2 Parallel Lines and Transversals

Geometry 3.2 Parallel Lines and Transversals Theorems in a nutshell. 2 lines ||  corr s  November 2, 2019 Geometry 3.2 Parallel Lines and Transversals

Geometry 3.2 Parallel Lines and Transversals Theorems in a nutshell. 2 lines ||  alt. int. s  November 2, 2019 Geometry 3.2 Parallel Lines and Transversals

Geometry 3.2 Parallel Lines and Transversals Theorems in a nutshell. 2 lines ||  alt. ext. s  November 2, 2019 Geometry 3.2 Parallel Lines and Transversals

Geometry 3.2 Parallel Lines and Transversals Theorems in a nutshell. 2 lines ||  SS int. s supp. November 2, 2019 Geometry 3.2 Parallel Lines and Transversals

Geometry 3.2 Parallel Lines and Transversals These are the “reasons” for proof. 2 lines ||  corr s  alt int s  alt ext s  ss int s supp November 2, 2019 Geometry 3.2 Parallel Lines and Transversals

Geometry 3.2 Parallel Lines and Transversals Sample problem 1 m n m || n (120 – x)° Solve for x. 5x° 2 lines ||  alt ext s  5x = 120 – x 6x = 120 x = 20 November 2, 2019 Geometry 3.2 Parallel Lines and Transversals

Geometry 3.2 Parallel Lines and Transversals Sample problem 2 m n m || n Solve for x. (x + 20)° (x + 8)° 2 lines ||  SS int s supp (x + 20) + (x + 8) = 180 2x + 28 = 180 2x = 152 x = 76 November 2, 2019 Geometry 3.2 Parallel Lines and Transversals

Geometry 3.2 Parallel Lines and Transversals Sample problem 3 m n m || n Solve for x. (x + 40)° (x + 40)° (x + 50)° Linear Pair Post. (x + 40) + (x + 50) = 180 2x + 90 = 180 2x = 90 x = 45 2 lines ||  corr s  November 2, 2019 Geometry 3.2 Parallel Lines and Transversals

Geometry 3.2 Parallel Lines and Transversals In Summary. 2 lines ||  corr s  alt int s  alt ext s  ss int s supp November 2, 2019 Geometry 3.2 Parallel Lines and Transversals

Geometry 3.2 Parallel Lines and Transversals Extra for Experts m n m || n x° 43° 25° Find x. November 2, 2019 Geometry 3.2 Parallel Lines and Transversals

Geometry 3.2 Parallel Lines and Transversals Solution m n m || n x° 43° 25° 25° 43° Find x. x° = 25° + 43° = 68° November 2, 2019 Geometry 3.2 Parallel Lines and Transversals