Question

determine if triangle efg and triangle hij are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.) answer attempt 1 out of 2 the triangles similar.

Explanation:

Step1: Calculate the ratio of corresponding sides

For triangle \(EFG\) and \(HIJ\), we have two pairs of corresponding sides:
\(\frac{12}{18}=\frac{2}{3}\) and \(\frac{10}{15}=\frac{2}{3}\)

Step2: Check the included angle

The included angles \(\angle G = 42^{\circ}\) and \(\angle J=42^{\circ}\) are equal.

By the Side - Angle - Side (SAS) similarity criterion, if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the two triangles are similar.

Answer:

The triangles are similar. By the SAS (Side - Angle - Side) similarity criterion, since \(\frac{EG}{HJ}=\frac{FG}{IJ}=\frac{2}{3}\) and \(\angle G=\angle J = 42^{\circ}\)