Question

which rule explains why these scalene triangles are similar?
(the image shows two scalene triangles, one with vertices e, g, f and sides eg = 72, gf = 48, and a right angle at g; the other with vertices s, r, t and sides sr = 54, rt = 36, and a right angle at r. the options are: sss, sas, aa, none of the above; the triangles cannot be proven similar)

Explanation:

Step1: Calculate side ratios

$\frac{EG}{SR} = \frac{72}{54} = \frac{4}{3}$, $\frac{FG}{TR} = \frac{48}{36} = \frac{4}{3}$

Step2: Verify included angles

$\angle G = \angle R$ (marked congruent)

Step3: Apply similarity rule

Two sides proportional, included angles congruent → SAS similarity.

Answer:

SAS