Video: Using Triangle Congruence Criteria to Establish Congruence

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.

02:26

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 weโ€™re presented with two triangles, triangles ๐ด๐ต๐ถ and ๐ด dash ๐ต dash ๐ถ dash, and asked to determine whether or not theyโ€™re congruent. Weโ€™re also given three possible congruence criteria. Remember here, S stands for side and ๐ด stands for angle.

Letโ€™s 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 ๐ด dash ๐ต dash in the first triangle and ๐ด๐ต in the second, so we have the statement ๐ด dash ๐ต dash is equal to ๐ด๐ต. 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 ๐ต dash ๐ถ dash in the first triangle and side ๐ต๐ถ in the second. So we have the statement ๐ต dash ๐ถ dash is equal to ๐ต๐ถ. 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 ๐ด dash ๐ถ dash in the first triangle and side ๐ด๐ถ in the second. So we have the statement ๐ด dash ๐ถ dash is equal to ๐ด๐ถ, and again the S in brackets to indicate itโ€™s a statement about a side.

Now looking at the three statements weโ€™ve 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 Sโ€™s as we wrote down our congruency statements tells us that itโ€™s 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.

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