Mid segment is basically connecting the midpoints of two sides of the triangle. So for example, if this length and this length are the same, that makes this the midpoint. If this segment and this segment are the same, that makes this the midpoint.
And if we connect those with a line segment, this is called the mid segment. And the interesting properties of the mid segment are that it's going to be parallel to this third side, okay, to the base, and it's going to be half the length, okay? So if this was 10, this would be 5, okay? So that's the idea.
So it's parallel and it's going to be half the length. Now if you find the midpoint of this side right here, okay, such that these are the same and you connect these two midpoints, this would be a mid segment and it's going to be parallel to this base and half as long and then same thing here if you connect these two midpoints, this is a mid segment. It's going to be half of this base and parallel.
Now another interesting property that sometimes students overlook is that, you know, because this length is half of the base, this segment this segment and this segment are all going to be the same length okay same thing over here if these are the same okay this mid segment is going to be the same and then if these two are the same these three are going to be the same okay so you're with me so far so let's look at a couple examples and we'll understand this a little bit better so here we've got a mid segment you can see that the these are the two mid points are connected there so if this is seven that means that the space must be double it must be 14 right Okay, example number two, a little bit different. We're combining algebra with geometry here. Here they're giving us this mid-segment.
Okay, so let's make sure that we just have that identified as the two midpoints. So how do we relate this quantity and this quantity? Well, we know that the mid-segment is half the base. So if we want to make an equation, an easy way to do this is to double the mid-segment and then set it equal to the base. So if we double x plus 4, then it will be equal to the base, which is 3x minus 6. So let's just distribute.
We get 2x plus 8 equals 3x minus 6. Let's see, subtract 2x from both sides. So that gives us x minus 6 equals 8, and we're going to add 6 to both sides. Okay, so that gives us x equals 14, and we got it.
So that's the idea. If you double the mid-segment, then they're going to be the same length, and you can set it equal to the base. So I hope this helps you to understand how to work with the mid-segment theorem better. Subscribe to the channel. Check out more math tutoring videos on Mario's Math Tutoring YouTube channel, and I look forward to helping you in the future videos.
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