Question

the triangles are similar by:
the sss similarity theorem.
the sas similarity theorem.
the aa similarity postulate.
the triangles are not similar.

Explanation:

Step1: Check side ratios

Calculate the ratios of corresponding sides. For triangle \(ABC\) and \(EDC\), the sides around the equal angles (\(x^\circ\)):
\(\frac{AC}{EC} = \frac{200}{320} = \frac{5}{8}\), \(\frac{BC}{DC} = \frac{150}{240} = \frac{5}{8}\).

Step2: Identify similarity criterion

We have two sides in proportion (\(\frac{AC}{EC} = \frac{BC}{DC}\)) and the included angle equal (\(x^\circ = x^\circ\)). This matches the SAS (Side - Angle - Side) similarity theorem, which states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, the triangles are similar.

Answer:

the SAS similarity theorem.