TenMarks teaches you how to prove lines parallel using corresponding and same side interior angles.
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Learn Corresponding and Same Side Interior Angles between Parallel Lines In this lesson, let’s learn how we identify if lines are parallel by looking at the corresponding and same-side interior angles. So the first problem and we’ll do two of them. One says, during a race all members of the rowing team, the picture shown here, should keep that oars which is the oars parallel to each side. So we’re saying this guy and this guy should have the oars are already parallel. We’re given measure of this angle, angle one is 3x+13 and measure of angle two is 5x-5 degrees. And we’re given X equals 9. We need to show these two oars are indeed parallel. So I’m actually going to simplify this and say this is the row boat and this is angle one and this angle two I’m just drawing the picture to make it easier for us to work on. So what we’re told is angle is 3x+13 degrees and angle two equals 5x-5 degrees. For these two lines to be parallel, let’s assume these two lines are parallel and at this line we’ll do intersect then angle and one and angle two should be equal. They would be corresponding angles so they would have to be equal. So if they’re equal let’s see if they are. If X equals nine so instead of nine let’s substitute X with 9 so three times nine is 27 plus 13 that is 40 degrees and five times nine is 45 minus five is 40 degrees. So we can see angle one as 40 degrees, angle two as 40 degrees which means by using the converse of the corresponding theorem we can say that these two lines are parallel because this line goes or same measurement. If two lines are intersected by a transversal and these two angles are equal that means these two lines were parallel to begin with. You get that? Now, let’s try one more using same-side interior angles. Here, what we’re given is measure of angle four is 79 degrees so this angle is 79 degrees. The measure of angle six, this one is 101 degrees, is line A parallel to line B which is this line and this line are they parallel? Well, these are same-side interior angles right? These are on the same side of the transversal and both are the interior sides so same-side interior angles. If these two lines are parallel then the sum of or the same-side interior angles must be complimentary which means should total 180 degrees so let’s check if they do. One angle is measure of angle four equals 79 degrees, measure of angle six is 101 degrees. If we add these two I get 180 degrees. So if angle four plus measure of six equals 180 degrees that means these two are same-side interior angles. Since they are 180 degrees the sum, then these are same-side interior angles, these two angles and if these are same-side interior that can only happen if these two lines are parallel so hence the lines are parallel.
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