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Geometry 3.2 Properties of Parallel Lines Postulate If two // lines are cut by a transversal, then corresponding angles are congruent. ~ // Lines => corr. <‘s = 2 1 4 3 5 7 6 8 Example: <1 =~ <5 Theorem If two // lines are cut by a transversal, then alternate interior angles are congruent. ~ // Lines => alt int <‘s = 2 1 4 3 5 7 6 8 Example: <3 =~ <6 We can prove this theorem using the previous postulate. Theorem If two // lines are cut by a transversal, then same side interior angles are supplementary. // Lines => SS Int <‘s supp 2 1 4 3 5 7 6 8 Example: <4 is supp to <6 Planning Its Proof If two // lines are cut by a transversal, then same side interior angles are supplementary. Given: k // n Prove: <1 is supp to <4 k 1 4 2 n Theorem If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line. Planning Its Proof If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line. Given: k // n; t Prove: t n k t 1 k 2 n Why is… ~ <4? …<5 = ~ // Lines => alt int <‘s = …<8 ~ = <4? ~ // Lines => corr. <‘s = …<5 supp to <3? …j t, if k t? // Lines => SS Int <‘s supp If a transversal is perp. to 1 of 2 // lines, it is perp. to both. t 2 1 4 3 5 7 6 8 k j Let’s do some from the HW together! Page 81-82 #11, #16, #18 HW Page 80-82 CE #2-9, WE 1-15 Odd, 18-21