Answer:
SAS theorem
Step-by-step explanation:
If [tex]\frac{CE}{CB} = \frac{DC}{AC}[/tex] and m∠ECD = m∠BCA, then the triangles are similar by the SAS theorem.
[tex]\frac{EC}{BC} = \frac{14}{21} = \frac{2}{3}[/tex] [tex]\frac{DC}{AC} = \frac{18}{27} = \frac{2}{3}[/tex]
So, [tex]\frac{CE}{CB} = \frac{DC}{AC}[/tex] and m∠ECD = m∠BCA because vertical angles are congruent
Therefore ΔECD is similar to ΔBCA by SAS theorem
