Question

which descriptions from the list below accurately describe the relationship between △ abc and △ def? check all that apply.

Explanation:

Step1: Check Angle Correspondence

In $\triangle ABC$ and $\triangle DEF$, we have $\angle B = \angle E = 120^\circ$, $\angle C = \angle F = 30^\circ$. By the Angle - Angle (AA) similarity criterion, the triangles are similar. Similar triangles have the same shape.

Step2: Check Side Ratios

For $\triangle ABC$: sides are $3,5,7$. For $\triangle DEF$: sides are $6,10,14$. Calculate the ratios: $\frac{6}{3}=2$, $\frac{10}{5}=2$, $\frac{14}{7}=2$. The sides are in proportion (scale factor of 2), so they are similar (not congruent as congruent triangles have equal side lengths, here sides of $\triangle DEF$ are twice that of $\triangle ABC$ so not same size). Similar triangles have the same shape.

Answer:

Similar, Same shape