### Video Transcript

Determine whether the triangles in the given figure are congruent by applying SSS, SAS, or ASA. If they are congruent, state which of the congruence criteria proves this.

So weโre presented with two triangles, triangles ๐ด๐ต๐ถ and ๐ด dash ๐ต dash ๐ถ dash, and asked to determine whether or not theyโre congruent. Weโre also given three possible congruence criteria. Remember here, S stands for side and ๐ด stands for angle.

Letโs look at the two diagrams and see what congruence statements we can write down. First, we see that both triangles have a length of three units. This side is ๐ด dash ๐ต dash in the first triangle and ๐ด๐ต in the second, so we have the statement ๐ด dash ๐ต dash is equal to ๐ด๐ต. The S in brackets is used to indicate that this is a statement about the length of a side.

Next, we see that both triangles have a length of five units, its side ๐ต dash ๐ถ dash in the first triangle and side ๐ต๐ถ in the second. So we have the statement ๐ต dash ๐ถ dash is equal to ๐ต๐ถ. And again, the S in brackets indicates that this is a statement about a side.

Finally, we see that both triangles have a length of 3.16 units, side ๐ด dash ๐ถ dash in the first triangle and side ๐ด๐ถ in the second. So we have the statement ๐ด dash ๐ถ dash is equal to ๐ด๐ถ, and again the S in brackets to indicate itโs a statement about a side.

Now looking at the three statements weโve made and comparing them to the congruence criteria, we can see that we do have enough information to conclude that these two triangles are congruent. The inclusion of the Sโs as we wrote down our congruency statements tells us that itโs the side-side-side, SSS, congruence criteria.

And so we have our answer to the problem: yes, the two triangles are congruent, and this is due to the side-side-side congruence criteria.