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What are Same Side Interior Angles?

You might have heard of alternate interior angles or even vertical angles, but what about same side interior angles? In this blog post, we’ll be taking a closer look at what same side interior angles are, how to identify them, and some of the properties they possess. By the time you’re finished reading, you’ll be an expert on same side interior angles!

Definition of Same Side Interior Angles.

Same side interior angles aredefined as a pair of angles that are located on the same side of a line segment and on the inside of that line segment. In order for two angles to be considered same side interior angles, they must also share a vertex. 

Properties of Same Side Interior Angles

Now that you know what are same side interior angles, let’s take a closer look at some of their properties. 

  • First, it’s important to note that same side interior angles are always equal to each other. This might not seem like a big deal, but it actually has some pretty interesting implications. 

For example, say you’re trying to find the value of an angle in a triangle and two of the sides intersect at a 90 degree angle. That means that the third angle must also be 90 degrees, since the sum of all the angles in a triangle must equal 180 degrees. So, if you know the value of two of the angles, you can easily determine the value of the third angle without having to do any complicated math. 

same side interior angles

This property also comes in handy when you’re working with parallelograms. Since opposite sides of a parallelogram are parallel, that means that all four of the angles must be equal. So, if you can determine the value of any one angle, you automatically know the value of all four angles. 

  • Another interesting property of same side interior angles is that they can be used to prove whether or not lines are parallel. If two lines are cut by a transversal and the resulting same side interior angels are equal, then those lines must be parallel! 

Unfortunately, there is one restriction to this method; it only works if all eight angles formed by the intersection are equal. If even just one pair of same side interior angles is not equal, then you can’t conclude that the lines must be parallel. However, if all eight angles ARE equal then you CAN conclude that the lines must be parallel regardless of whether or not any pairs of opposite sides are equal (i.e., it doesn’t matter if the parallelogram is a rectangle or not). 

Conclusion

Next time someone asks you about geometry, impress them with your knowledge of same side interiorangles! These seemingly mundane concepts actually have some pretty interesting properties that make them unexpectedly useful in day-to-day life. Knowing about things like this might just help you gets those top marks in your next math test!

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