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**3.3 Proving Lines Parallel**

Geometry 3.3 Proving Lines Parallel

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**Postulate From yesterday :**

~ From yesterday : If two // lines are cut by a transversal, then corresponding angles are congruent. // Lines => corr. <‘s = 1 2 3 4 5 6 7 8 ~ <1 = <5

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**Postulate Today, we learn its converse :**

If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. ~ corr. <‘s = => // Lines 1 2 3 4 5 6 7 8 ~ // If <1 = <5, then lines are

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**Theorem From yesterday:**

~ From yesterday: If two // lines are cut by a transversal, then alternate interior angles are congruent. // Lines => alt int <‘s = 1 2 3 4 5 6 7 8 ~ Example: <3 = <6

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**Theorem Today, we learn its converse :**

If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel. ~ alt int <‘s = => // Lines 1 2 3 4 5 6 7 8 ~ // If <3 = <6, then lines are

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**Theorem From yesterday:**

If two // lines are cut by a transversal, then same side interior angles are supplementary. // Lines => SS Int <‘s supp 1 2 3 4 5 6 7 8 Example: <4 is supp to <6

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**Theorem Today, we learn its converse :**

If two lines are cut by a transversal and same side interior angles are supplementary, then the lines are parallel . SS Int <‘s supp => // Lines 1 2 3 4 5 6 7 8 If <4 is supp to <6, then the lines are //

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**Theorem From yesterday:**

If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.

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**Theorem t Today, we learn its converse:**

In a plane two lines perpendicular to the same line are parallel. t k l If k and l are both to t then the lines are //

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3 More Quick Theorems Theorem: Through a point outside a line, there is exactly one line parallel to the given line. Theorem: Through a point outside a line, there is exactly one line perpendicular to the given line. Theorem: Two lines parallel to a third line are parallel to each other. . .

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**Which segments are parallel ?…**

Are WI and AN parallel? No, because <WIL and <ANI are not congruent 61 ≠ 62 22 23 61 62 L I N E Are HI and TN parallel? Yes, because <WIL and <ANI are congruent = 84 = 84

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**In Summary (the key ideas)………**

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**5 Ways to Prove 2 Lines Parallel**

~ Show that a pair of Corr. <‘s are = √ √ √ √ √ Alt. Int. <‘s are = √ √ √ √ √ S-S Int. <‘s are supp Show that 2 lines are to a 3rd line √ √ √ √ √ to a 3rd line ~

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Turn to pg. 87 Let’s do #19 and # 28 from your homework together

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Homework pg. 87 # 1-27 odd

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Proving Lines Parallel Section 3-5. Postulate 3.4 If 2 lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.

Proving Lines Parallel Section 3-5. Postulate 3.4 If 2 lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.

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