Question

is $\triangle gyk$ similar to $\triangle bak$?
yes
no

Explanation:

Step1: Check Vertical Angles

$\angle GKY$ and $\angle BKA$ are vertical angles, so $\angle GKY = \angle BKA$.

Step2: Check Side Ratios

For $\triangle GYK$ and $\triangle BAK$:

• $\frac{GK}{BK} = \frac{10}{6} = \frac{5}{3}$
• $\frac{YK}{AK} = \frac{25}{15} = \frac{5}{3}$
• $\frac{GY}{BA}$ (we can check if ratios are equal, and since two sides are in ratio and included angle equal, by SAS similarity, triangles are similar. Also, $\frac{10}{6}=\frac{25}{15}=\frac{5}{3}$, and included angle equal, so similar.

Answer:

Yes (the "Yes" option should be selected, as the triangles have proportional sides and equal included angles, satisfying SAS similarity criterion.)