Final answer:
To show that triangles APQR and APTS are similar using the SSS similarity theorem, we verify that the ratios of the corresponding sides are equal, AP/AQ = AR/AS = PQ/PT, thus confirming their similarity and the corresponding angles being congruent.
Step-by-step explanation:
To show that triangles APQR and APTS are similar using the SSS similarity theorem, we must demonstrate that the ratios of the corresponding sides of the triangles are equal. The SSS similarity theorem states that if the corresponding sides of two triangles are proportional, then the triangles are similar.
Let's assume we're given that the corresponding sides are proportional, that is, AP/AQ = AR/AS = PQ/PT. From this, according to the SSS similarity theorem, we can conclude that triangle APQR is similar to triangle APTS. To show this, we can write the ratios of the corresponding sides of the triangles as AP/AQ = AR/AS = PQ/PT. Each of these ratios should equal the same constant of proportionality if the triangles are indeed similar.
In practice, the values of these sides would be provided, and after calculating each ratio, the equality of the ratios confirms the similarity of the triangles. The congruence of the corresponding angles is then implied by the corresponding sides being proportional.