 In this video, I'm going to talk about the properties of congruence. Now, these properties are going to be very similar to the properties of the quality video that I did earlier, except for we're going to use congruency symbol, and we're going to use shapes. Now, for these examples that I have, I'm going to use the segment AB. I'm going to use the segment CD, and I'm going to use the segment EF. Now, these are just arbitrary segments that I'm going to use for my definitions here. Now, again, with congruency, congruency has to deal with shapes, and figures, and lines, and that sort of thing, whereas equality usually just has to deal with numbers. The reflexive property of congruence looks a little bit like this. AB is congruent to itself AB. The reflexive property is basically saying that a shape is going to be congruent to itself. The size and the shape of that shape, whatever it might be, is going to be the same, which, again, sounds a little bit redundant, but that's what the reflexive property is. Symmetric property of congruence, on the other hand, a little bit different. I'm going to use a conditional statement here, an if-then statement. If the segment AB is congruent to the segment CD, then I also know that the segment CD is going to be congruent to the segment AB. Notice everything gets flip-flopped there. That's what the symmetric property is, is that these kind of get flipped around. Again, we're using the congruency symbol instead of the inequality symbol like earlier with the equality statements. Last but not least, transitive property of congruence. This one's a little bit longer, and I'm going to use all three of my statements up here. If the segment AB is congruent to the segment CD and, another statement here, if the segment CD is congruent to the segment EF, so we're using three different segments here, then the segment AB is also going to be congruent to the segment EF. So notice this one's the big jump. AB is congruent to CD, CD is congruent to EF, therefore AB is going to be congruent to EF, making the big jump from the first to the last, first statement to the last. So that is the transitive property of congruence. What we're going to do now is I'm going to go over a couple of examples using these. So this is identifying properties of equality and congruence. So now we're going to kind of compare and contrast either the equality statements or the congruency statements and kind of look to see what the difference between them are. Okay, so I'm supposed to identify the property that justifies each statement. Now remember, we can use either congruency statements or we can use equality statements. It all depends on what is shown. Okay, first example, we have the angle QRS is congruent to the angle QRS. Well, that tells me right away that that's reflexive property. Reflexive says that an angle is going to be equal or congruent to itself. Reflexive property of, now this is where I stop. Is this equality or is it congruency? Now if I look at my problem, I see a congruency symbol. So this is definitely going to be a property of congruency. Okay, so again, part of this is not only identifying the property, but I also correctly identifying if it's equality or congruency. Alright, so let's take a look at the next example. The measure of angle one is equal to the measure of angle two. So the measure of angle two is equal to the measure of angle one. Sounds pretty simple. So this what it looks like is happening is I'm flip-flopping the two's and the one's. Flip-flopping the two's and the one's. This looks like the symmetric property. Symmetric property of and stop again. Now is this equality or is this congruency? Now as I look through the statement, I see equal signs all over the place. That's a dead giveaway. This is going to be a property of equality. Property of equality. Okay, so last third example down here. We have that the segment AB is congruent to the segment CD and the segment CD is congruent to the segment EF. So AB is then congruent to EF. Now we just went over this a moment ago on the previous slide. This is going to be the transitive property. So transitive property. Now of equality, equality or congruence. Now we're talking about shapes here. We're talking about shapes, but we need to look at the symbols that we're using. We're using congruency symbols here. So this is going to be the transitive property of congruency. Okay, and there's just a couple of examples kind of showing the difference between congruency statements one and three were congruency statements and then number two was an equality statement. Number two is an equality statement. Okay, those are the congruency properties and then just an example going over the differences between those different properties.