Question

quiz 3
g x y
10 25
15 k
6
a 12 b
the triangles are similar by
the sss similarity theorem.
the sas similarity theorem.
the sss similarity theorem and the sas similarity theorem
they triangles are not similar

Explanation:

Step1: Identify Corresponding Sides

First, we check the ratios of corresponding sides. For triangle \( \triangle ABK \) and \( \triangle GYK \):

• \( \frac{AB}{GY}=\frac{12}{x} \), \( \frac{BK}{GK}=\frac{6}{10}=\frac{3}{5} \), \( \frac{AK}{YK}=\frac{15}{25}=\frac{3}{5} \).

Step2: Check SAS Similarity

We have two sides in proportion (\( \frac{BK}{GK}=\frac{AK}{YK}=\frac{3}{5} \)) and the included angle (vertical angles at \( K \) are equal). So by SAS (Side - Angle - Side) similarity theorem, the triangles are similar.

Answer:

The SAS similarity theorem (the option with "the SAS similarity theorem")