Geometry 3 3 Proving Lines Parallel Postulate From

Postulate ~ From yesterday : // Lines => corr. <‘s = If two //

Postulate Today, we learn its converse : If two lines are cut by a

Theorem From yesterday: // Lines => alt int <‘s ~= If two // lines

Theorem Today, we learn its converse : If two lines are cut by a

Theorem // Lines => SS Int <‘s supp From yesterday: If two // lines

Theorem From yesterday: If a transversal is perpendicular to one of two parallel lines,

Theorem Today, we learn its converse: In a plane two lines perpendicular to the

3 More Quick Theorems Theorem: Through a point outside a line, there is exactly

Which segments are parallel ? … Are WI and AN parallel? W No, because

5 Ways to Prove 2 Lines Parallel 1. ~ Show that a pair of

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

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Geometry 3. 3 Proving Lines Parallel

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

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 2 1 4 3 5 7 6 8 If <1 ~ = <5, then lines are //

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

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 2 1 4 3 5 7 6 8 ~ If <3 = <6, then lines are //

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

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 4 3 5 7 2 1 6 8 If <4 is supp to <6, then the lines are //

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

Theorem 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 //

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. . .

Which segments are parallel ? … Are WI and AN parallel? W No, because <WIL and <ANI are not congruent A H T 22 23 61 ≠ 62 61 Are HI and TN parallel? Yes, because <WIL and <ANI are congruent 61 + 23 = 84 62 + 22 = 84 L 62 I N E

In Summary (the key ideas)………

5 Ways to Prove 2 Lines Parallel 1. ~ Show that a pair of Corr. <‘s are = ~ 2. √ √ √ Alt. Int. <‘s are = 3. √ √ √ S-S Int. <‘s are supp 4. 5. Show that 2 lines are √ √ √ to a 3 rd line

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

Homework pg. 87 # 1 -27 odd