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 \(EDC\), \(\frac{BC}{DC}=\frac{150}{240}=\frac{5}{8}\), \(\frac{AC}{EC}=\frac{200}{320}=\frac{5}{8}\).

Step2: Check included angle

The included angle for these sides is \(x^\circ\) for both triangles, so the included angles are equal.

Step3: Apply SAS similarity

Since two sides are in proportion and the included angle is equal, by SAS (Side - Angle - Side) similarity theorem, the triangles are similar.

Answer:

the SAS similarity theorem (the option with "the SAS similarity theorem")