Question

sss ~ determine if the triangles are similar by side-side-side similarity

1. diagrams of triangles with side lengths: first triangle n-r-x with sides 13.5, 27, 9; second triangle s-d-e with sides 42, 21, 14; third figure with w-x-y-u-v with sides 15, 6, 20, 40, 56, 8

Explanation:

Step1: Check triangle 1 (leftmost)

Sides: 9, 13.5, 27. Ratios: $\frac{9}{13.5}=\frac{2}{3}$, $\frac{13.5}{27}=\frac{1}{2}$ → Not equal.

Step2: Check triangle 2 (middle)

Sides: 14, 21, 42. Ratios: $\frac{14}{21}=\frac{2}{3}$, $\frac{21}{42}=\frac{1}{2}$ → Not equal.

Step3: Check triangle 3 (rightmost)

Sides: 20, 40, 56; 8, 16, 56? No, right triangle sides: 20, 40, 56? Ratios: $\frac{20}{8}=\frac{5}{2}$, $\frac{40}{16}=\frac{5}{2}$, $\frac{56}{56}=1$ → Not equal.

Answer:

None of the triangles are similar by SSS similarity.