How can the triangles be proven similar by the sss similarity theorem?

Similarity can be proven, either by SSS, SAS, or AAS.

Answer: Triangles ABC and QPR are both similar by SSS since the ratio of their corresponding sides is equal.

Various properties can be used once the similarity is proven, on both the triangles taken into consideration.

Explanation:

To prove 2 triangles similar using, SSS similarity.

Let us consider two triangles UVW and XYZ

                               (Triangles to be proven similar)

Step 1: Find the different ratios of the two triangles' sides and compare till each of the ratios becomes the same. Then compare the Ratios, and bring about the equal ones, suppose:

UV / XY = 5 / 4  , VW / ZY = 5 / 4 ,  WU / XZ = 5 / 4

Thus all three ratios are same and equal to 5 / 4.

Step 2: Now we can state the theorem of similarity by S.S.S ( Side, side, side ) the triangles UVW and XYZ are both similar to each other.