Question

quiz

is \\(\triangle gyk\\) similar to \\(\triangle bak\\)?

\\(box\\) yes
\\(box\\) no

Explanation:

Step1: Check Right Angles

Both \(\triangle GYK\) and \(\triangle BAK\) have a right angle (since \(GB\) is vertical and \(AB\) is horizontal, so \(\angle G\) and \(\angle B\) are right angles).

Step2: Check Proportional Sides

For \(\triangle BAK\), sides are \(AB = 12\), \(BK = 6\), \(AK = 15\). For \(\triangle GYK\), \(GK = 10\), \(YK = 25\), \(GY=x\).
Check ratios: \(\frac{BK}{GK}=\frac{6}{10}=\frac{3}{5}\), \(\frac{AB}{GY}\) (wait, better to check \(\frac{BK}{GK}=\frac{6}{10}=\frac{3}{5}\), \(\frac{AK}{YK}=\frac{15}{25}=\frac{3}{5}\). Also, \(\angle AK B=\angle YK G\) (vertical angles). By SAS similarity, if two sides are proportional and included angle equal, triangles are similar. Since \(\frac{BK}{GK}=\frac{AK}{YK}=\frac{3}{5}\) and \(\angle K\) is common (vertical angles, so equal), the triangles are similar.

Answer:

Yes