Question

are the following similar? why or why not? no, the ratios of the corresponding sides are not equal. yes no, the corresponding angles are not equal.

Explanation:

Step1: Check the angles

In \(\triangle ABC\) and \(\triangle DEF\), \(\angle A=\angle D = 70^{\circ}\), \(\angle B=\angle E = 40^{\circ}\). By the angle - sum property of a triangle (\(\angle A+\angle B+\angle C=180^{\circ}\), \(\angle D+\angle E+\angle F = 180^{\circ}\)), we can find \(\angle C=\angle F=70^{\circ}\). So the corresponding angles are equal.

Step2: Check the side - ratios

The ratio of the sides: \(\frac{AB}{DE}=\frac{27}{36}=\frac{3}{4}\), \(\frac{AC}{DF}=\frac{18}{24}=\frac{3}{4}\), \(\frac{BC}{EF}=\frac{27}{36}=\frac{3}{4}\). The ratios of the corresponding sides are equal.

Answer:

Yes