Question

quiz 3
the triangles are similar by:
○ the sss similarity theorem
○ the sas similarity theorem
○ the sss similarity theorem and the sas similarity theorem
○ the triangles are not similar
(diagram with triangles: a, b, k, g, y; lengths: ak=15, kb=6, gk=10, yk=25, gy=x)

Explanation:

Step1: Check the ratio of sides

We know that \(\frac{GK}{BK}=\frac{10}{6}=\frac{5}{3}\), \(\frac{YK}{AK}=\frac{25}{15}=\frac{5}{3}\)

Step2: Check the included angle

\(\angle GKY\) and \(\angle BKA\) are vertical angles, so \(\angle GKY=\angle BKA\)

Since two sides are in proportion (\(\frac{GK}{BK}=\frac{YK}{AK}\)) and the included angles are equal (\(\angle GKY = \angle BKA\)), by the SAS (Side - Angle - Side) similarity theorem, \(\triangle GKY\sim\triangle BKA\)

Answer:

the SAS similarity theorem