Question

triangle abc with side ab=12, angle at b=50°, side bc=24; triangle fde (or fue) with side fu=8, angle at f=50°, side fe=16. options: sss, sas, aa, aas

Explanation:

Step1: Check side ratios

Calculate ratios of corresponding sides. For triangle \(ABC\) and \(F...\) (let's assume the other triangle is \(FDE\) for clarity):
\(\frac{AB}{FD}=\frac{12}{8} = \frac{3}{2}\), \(\frac{BC}{FE}=\frac{24}{16}=\frac{3}{2}\).

Step2: Check included angle

Angle \(B\) and angle \(F\) are both \(50^\circ\), and they are included between the sides with the same ratio.

Step3: Identify similarity criterion

The SAS (Side - Angle - Side) similarity criterion states that if two sides of one triangle are in proportion to two sides of another triangle, and the included angles are equal, the triangles are similar. Here, two sides are proportional (\(\frac{3}{2}\)) and the included angle (\(50^\circ\)) is equal. So the similarity criterion is SAS.

Answer:

SAS (assuming the option with "SAS" is the correct one; if options are labeled, e.g., if "SAS" is option B, then "B. SAS")