Question

show that the triangles are similar and write a similarity statement.

so ( \triangle a b c sim \triangle square )

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. So \(\angle ACB\cong\angle ECD\)

Step2: Calculate the ratios of corresponding sides

We have \(CE = 14\), \(AC=27\), \(DC = 18\), \(BC = 21\)
The ratio \(\frac{CE}{BC}=\frac{14}{21}=\frac{2}{3}\) and \(\frac{DC}{AC}=\frac{18}{27}=\frac{2}{3}\)

Step3: Use the Side - Angle - Side (SAS) similarity criterion

Since \(\angle ACB\cong\angle ECD\) and \(\frac{CE}{BC}=\frac{DC}{AC}\), by the SAS similarity criterion, \(\triangle ABC\sim\triangle DEC\)

Answer:

\(\angle ACB\cong\angle ECD\), \(\frac{CE}{BC}=\frac{DC}{AC}\), \(\triangle ABC\sim\triangle DEC\)