Question Video: Looking Closely at the Side-Angle-Side Criterion Mathematics

Video Transcript

Can you use SAS to prove the triangles in the given figure are congruent? Please state your reason.

Two triangles are congruent if their corresponding sides are congruent and corresponding angles are congruent. Here, we are specifically asked if we can use the congruence criterion SAS to prove this. If we look at the measures that we’re given in this diagram, we can say that 𝐴𝐵 is equal to 𝐴 prime 𝐵 prime because they’re both given as 2.36 length units. And 𝐴𝐶 is equal to 𝐴 prime 𝐶 prime because these lengths are both given as 5.52 length units. We also have a corresponding pair of angle measures that are congruent. The measure of angle 𝐴𝐶𝐵 and the measure of angle 𝐴 prime 𝐶 prime 𝐵 prime are both given as 25.22 degrees.

The SAS congruence criterion tells us that two triangles are congruent if they have two congruent sides and an included angle congruent. But in this figure, the angle which we are given in each triangle is not the included angle between the two sides. For the included angle here, we would need to be able to know and compare the measure of angle 𝐶𝐴𝐵 and the measure of angle 𝐶 prime 𝐴 prime 𝐵 prime. When we give our answer for this question, a good answer needs to reference the fact that we can’t say the triangles are congruent because the angle that we are given is not the appropriate angle. Therefore, to answer the question “Can we use SAS to prove the triangles are congruent?,” we can say no, because the angle must be contained or included between the two sides.