PARALLEL LINES AND TRIANGLES WEDNESDAY OCTOBER 29

1. Using Triangle Angle-Sum Theorem, solve for x 2. Using Linear Pairs, solve for y 3. Using Triangle-Sun Theorem, solve for z WARM UP

And now… In honor of Halloween… A video of a very talkative porcupine eating tiny pumpkins… WARM UP

So yesterday we talked about the sum of the interior angles being equal to 180 degrees. But the homework questions had you answer for a couple of angles outside of the triangle TRIANGLE ANGLE-SUM THEOREM

In the case of the triangle to the right, if we know angle 2 then we know angle 1, because they are supplementary. TRIANGLE ANGLE-SUM THEOREM

But angle 1 has an even more important role: it can tell us sum of the other two angles. TRIANGLE ANGLE-SUM THEOREM

First some terminology. ∠ 1 is called an exterior angle. It is the angle formed by a side and a linear extension of the adjacent side TRIANGLE ANGLE-SUM THEOREM

The two interior angles that are not adjacent to ∠ 1 are called the remote interior angles. They are marked 38° and 70° in this case. TRIANGLE ANGLE-SUM THEOREM

So why do we care about an exterior angle and the two interior angles that aren’t adjacent to it? Because the measure of the two remote interior angles equals the measure of the exterior angle. TRIANGLE ANGLE-SUM THEOREM

The measure of the sum of the two remote interior angles of a triangle ( ∠ A and ∠ B) equals the measure of the exterior angle ( ∠ 1) THEOREM 3.11

Let’s go back to the example I showed at the beginning. We know using the Triangle Angle-Sum Theorem that m ∠ ° + 70° = 180° Therefore ∠ 2 measures 72°

THEOREM 3.11 And because 1 and 2 are a linear pair and therefore supplementary m ∠ 1 + m ∠ 2 = 180° 72° + m ∠ 1 = 180° Therefore ∠ 1 measures 108°…

THEOREM 3.11 Which is the sum of the remote interior angles. So this is one more weapon in the arsenal of solving for unknown angles in a triangle.

EXAMPLE Solve for x x° (x + 20)°150°

EXAMPLE 150 = (x) + (x + 20) 2x + 20 = 150 2x = 130 or x = 65 x° (x + 20)°150°

Do Now: Triangle Worksheet Remember I expect every student to participate! Referrals are written for people who choose to not participate. When Done: Start on homework, Problems 15-20, page HOMEWORK