TenMarks teaches you how to prove lines parallel using alternate interior and alternate exterior angles.
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Learn about Alternate Interior and Alternate Exterior Angles In this lesson, let’s understand the real life applications of alternate interior and alternate exterior angles. We’ll do two different problems. The first one shows us a fire escape outside a building. It says, in the fire escape measure of angle one which is this angle, measure of angle one equals 17x+9 degrees, measure of angle two, this angle right here is 14x+18 degrees, and we’re given X equals three. We need to show that these two landings are parallel. Well, what angles are these if I look at this angle? If these two lines are indeed parallel, let me draw this it way. This is one landing, this is the other landing. We’ve got a line like this, this is angle two, this angle one. If these two lines are parallel then these are alternate interior angles. If these two lines are parallel then one and two are alternate interior angles. And alternate interior angles are congruent which means they have same measurement. So let’s check if the measurement is the same. Let’s substitute X let’s put three so 17 times three is 51 plus nine equals 60 degrees. Here, 14 times three is 42 plus 18 equals 60 degrees. So these two angles are the same, this is 60 degrees, this is 60 degrees then by the theorem if two parallel lines are intersected by a transversal the alternate interior angles are equal. Alternatively, the reverse is also true. If two lines have a line cutting across them and the alternate interior angles happened to be equal then these two lines are parallel. So are these lines parallel? Yes, this is absolutely true. Let’s try the second problem. In this figure, we are given the measure of angle one is 54 degrees, this is 54 degrees. The measure of angle eight is 7x+5 degrees and we’re given x is seven so instead of X let’s put seven. Seven times seven is 49 plus five is 54 degrees. So what am I told? Angle one equals angle eight. Now, let’s look how did these angles behave. Well, if these two lines and they’re parallel then these two angles will be equal. So if A is parallel to B then angle one equals angle eight or if angle one equals angle eight, if these two angles are the same these are alternate exterior angles. If the two alternate exterior angles are equal then A is parallel to B. Since we know that these two are both 54 degrees we can conclude that A is parallel to B, this is indeed true.