 Let's take a look at this next one. Again, we're dealing with two triangles that we want to prove congruent, so let's name them So we can call them triangle TON and triangle FUN as in Proof is a ton of fun. All right, so we want to first prove our TF and OU BISECT each other. What does that mean? Well this word bisect BISECT means cut in half. So TF and OU cut each other in half In other words, TF refers to that long segment. TF is cut into two equal parts Similarly, OU is cut into two equal parts So now we have two pairs of sides. We've got the reds and the blues that's side and side and Right now we're missing a piece, right? We could either use side side side angle side And so we're missing a piece, but the way that the shape is drawn. We've got these vertical angles and Vertical angles are always congruent And so therefore we're going to prove that these two triangles are congruent using the side angle side theorem So let's get started So we know what it is we want to prove we want to prove that triangles TON and FUN are congruent and We agreed we're going to use the side angle side congruence theorem So we can talk about a pair of sides that are congruent a pair of angles that are congruent and Another pair of sides that are congruent in each of those boxes. So let's start with the reds. I Know that UN and ON are congruent Next the other pair of sides the blues those blue sides are congruent and finally the angles the angles up the middle Angle TNO and FNU Okay, so why are all of these segments congruent the red segments UN and ON? Why are they congruent? Well, they're congruent because TF and OU bisect each other and What that means is I know that TF bisects OU Also OU bisects TF So for the red segments to be congruent which segment is doing the bisecting and which is being bisected That's an important question in this case TF is doing the bisecting and OU is being bisected The opposite is true for the blue segments TN and FN in that case OU is doing the bisecting and TF is being bisected Now the connector reason you have to ask yourself. What does bisect mean? Well bisect means cuts in half And so for each of these reasons we're going to use the segment bisector definition And lastly we need to talk about where those green angles came from the green angles came from the vertical angles and always vertical angles Are congruent so we need a box that says hey I have vertical angles and then the box below it can say that they're congruent So there's the statement TNO FNU are vertical angles and as a result Vertical angles are congruent So the statement is if we have vertical angles Then those angles those vertical angles are congruent Super we're done