TenMarks teaches you how to identify angle pairs formed by a transversal.
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Learn about Angle Pairs Formed by a Transversal In this lesson, let’s learn about angle pairs that are formed when we use a transversal. So a transversal is a line shown here is the line T that intersects to other lines. So in this case, transversal (t) intersects a and b, this is line a, this is line b. We need to identify the corresponding angles, alternate interior, alternate exterior, vertical and same-side interior angles. So let’s do them one by one. First, let’s do vertical angles because that’s easy. Vertical angles are angles that are non-adjacent angles that are result of intersection of two lines. I’ll show you an example. So here’s one line a and here’s the line T. These two lines intersect so the angles that are not adjacent which means they’re not next to each other so two and three are next to each other, the three and four are next to each other but one and three are not next to each other. So these are not adjacent angles which means they’re not next to each other they’re across from each other, these are called vertical angles. So in this figure which ones are vertical? We have—one and three are then we’ve got two and four and here I’ve got five and seven and then we’ve got six and eight. So these are the vertical angles, opposite angles. Now, let’s look at—I’m going to erase the markings that I did. Now, let’s change the pen color and look at alternate interior and alternate exterior angle so alternate interior angles are angles that are on the interior side. You see these two lines this is called the interior, this area is called the exterior. So alternate interior means the transversal, if the angles are on opposite side of the transversal which is alternating angles one is on the side, one is on the side and both are in the interior, these are called alternate interior angles. So four and six is one example of alternate interior angles and that of course we’ve got three and five. So there are two pairs of alternate interior angles. Similarly, if you want to do alternate exterior it would be exactly the same right except it would be alternate exterior angles. So one and seven—let me erase the markings let me show you. So alternate would be on one side of the transversal, another side of the transversal but it has to be both angles in the exterior side. Do you notice this is exterior, this is exterior? So one and seven are alternate exterior similarly two and eight are alternate exterior angles. You get the idea. Now, the last thing I want to show is same-side interior angles. Same-side interior well let’s try to understand what it means. Same-side interior is—well, they have to be on the same set of the transversal as it said alternate is alternate side of the transversal, same-side interior is on the same side of the transversal but interior. So same side interior would be four and five so four and five would be same-side interior similarly would be three and six. You get the idea, right? So three and six are also same-side interior angles. The key thing to remember when identifying this is they give us the solution in the wording anyway. When they say same-side they’re always referring to the side of the transversal which side is on so these two are on the same side. When it’s adjacent that means they’re angles next to each other, those are easy. Vertical angles are angles that across from each other and alternate interior and alternate exterior are angles which are alternate but both in the interior side or both on the exterior side.