Question

here are triangles abc and dec. are triangles abc and dec similar? yes. no. explain or show your reasoning.

Explanation:

Step1: Find the ratio of corresponding sides

For \(\triangle ABC\) and \(\triangle DEC\), we have \(\frac{EC}{BC}=\frac{6}{6 + 12}=\frac{6}{18}=\frac{1}{3}\), \(\frac{DC}{AC}=\frac{2}{2+4}=\frac{2}{6}=\frac{1}{3}\).

Step2: Check the included angle

\(\angle ECD=\angle BCA\) (vertically - opposite angles)

Since the ratios of two pairs of corresponding sides are equal (\(\frac{EC}{BC}=\frac{DC}{AC}=\frac{1}{3}\)) and the included angles are equal (\(\angle ECD=\angle BCA\)), by the Side - Angle - Side (SAS) similarity criterion, \(\triangle ABC\sim\triangle DEC\)

Answer:

Yes.