Learn about Congruence and Similarity In this lesson let’s learn about congruence and similarity. We will learn how to tell whether the figures are congruent, similar or neither. We’ll use three different examples. Before we start with the problems let’s learn what makes figures congruent. So, when we talk about figures being congruent what we are saying is they have the same shape and they have the exact same size. So, size and shape both have to be exactly the same. The figures could be turned around differently. It could be colored differently but in order for them to be congruent they have to be the exact shape and size. In order for them to be similar, we just need to have the same shape. They could be of different sizes. The shape needs to be the same. So, let’s look at the examples on the left. In the first example we are given two squares. The first square is ABCD. The second square is PQRST. We can see that both of these have exactly the same shape. They have the same shape. They are both squares. Well, are they the same size? Let’s count the number of squares. They’re both five squares left and five squares down. So, they have exactly the same size as well which makes these two figures congruent. That’s one example. Let’s look at the second one. In this case, we are given two different triangles. Well, the shape of the triangle is the same. The shape of the triangle and both the triangles are the same but they are of different sizes. Sizes are not the same. The line XY is much bigger than line LM and all the other two lines are exactly the same. So, if you look at these two figures, they are similar. That is true but we can say that the angles are congruent. So, this angle XYZ is congruent to angle LMN because the angles are both 90 degrees. The size of this angle and this angle is exactly the same and so are the angles X and angle L. They are congruent, so the angles are congruent but the sizes of the line segments that make up the triangles are different. That’s the reason these triangles are similar and not congruent. Now, when we look at the third example, we can see we’ve got a pentagon and a hexagon. These are not the same shape which means that these are neither congruent nor similar. The way we denote a similar by the way, is we say we use this figure. So, in this case with the triangle XYZ is similar to triangle LMN. Again to recap, for two figures to be congruent, they must have the exact same shape and the exact same size as we can see with the two squares here. If the sizes are different but the shape is the same then we call them similar figures.