![]() So one way I could try to simplify this is to essentially cross multiply, that's equivalent to Now, really what I need to do is figure out how do IĪlgebraically manipulate it so I get what I have up here. Is the length of segment AD, AD plus segment DB, plus D B. So AE's length plus EC's length, and then this is going to be equal to the length of segment AD over segment AB, its length This is the same thingĪs the ratio of AE over, AC is AE plus EC's length. Just gonna start writing it to the right here to save space. The length of that segment to the length of the entire thing, to AB. Of the length of segment AE to this entire side to AC, is equal to the ratio of AD, And then given that these two are similar, then we can set up a proportion. And so we can say that triangle AED is similar to triangle ACB, ACB by angle similarity. You actually have a third because angle, I guess you call it BAC is common to both triangles. Here, if you care about it, but two is enough, but Of corresponding angles, that means that all of Sets of corresponding angles that are congruent. Triangle AED and triangle ACB, you see that they have two This time we have a different transversal, corresponding angles where a transversal Once again, because theyĪre corresponding angles. And we also know that angle two is congruent to angleįour for the same reason. I'm just trying to writeĪ little bit of shorthand. ![]() And the reason why, is because they are corresponding,Ĭorresponding angles. Two corresponding angles are going to be congruent. Two lines are parallel, we can view segment AC as a transversal intersecting So how do we do that? Well, because these So the way that we can try to do it is to establish a similarity between triangle AED and triangle ACB. This statement right over here, and what I underlined up here are equivalent given this triangle. The length of segment AD over the length of segment DB. Length of segment AE over the length of segment EC is going to be equal to Two sides proportionately, if we look at this triangle over here, it would mean that the So another way to say that it divides the other Original triangle side that is on one side of the dividing line to the length on the other side is going to be the same on both sides that it is intersecting. Way of writing it, another way of saying it divides the other two sides proportionately, is that the ratio between the part of the Over here on this triangle, we need to prove another So really given what we know, and what's already been written That is a line or a line segment that is parallel to one And you might wanna leverage this diagram. To one side of a triangle, then it divides the other We're asked to prove that if a line is parallel
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