Question Video: Using Triangle Congruence Criteria to Establish Congruence Mathematics

Which congruency criterion can be used to prove that the two triangles in the given figure are congruent? [A] SAS [B] ASA [C] SSS

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Video Transcript

Which congruency criterion can be used to prove that the two triangles in the given figure are congruent? Option (A) SAS, option (B) ASA, option (C) SSS.

In this question, we’re asked how we might determine if the two triangles are congruent. We can see some examples of some criterion that we could use. We can recall that the S represents a side and A would represent angle. So let’s look at our diagram and see if we can determine any corresponding pairs of sides or angles which are congruent.

We can see the length 𝐴𝐢 is 5.52. And this would be congruent with the line 𝐴 prime 𝐢 prime. So we have a pair of corresponding congruent sides. The line 𝐴𝐡 is marked as 1.93, and so is the line 𝐴 prime 𝐡 prime. So we have another pair of corresponding sides. The final two pairs of sides, 𝐡𝐢 and 𝐡 prime 𝐢 prime, are marked as 3.75, the same length. Showing that three pairs of corresponding sides are congruent would demonstrate that two triangles are congruent. Therefore, the congruency criterion which we could use is the SSS rule, and that was given in option (C).

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