Question

1. determine whether or not the pair of triangles is similar. if they are similar, state the similarity theorem and show how you know. if not, state why. is \\( \triangle tau \sim \triangle bac \\), why?

Explanation:

Step1: Check the ratio of corresponding sides

Calculate the ratios of the sides. For \(\triangle TAU\) and \(\triangle BAC\), \(\frac{TA}{BA}=\frac{21}{7} = 3\), \(\frac{AU}{AC}=\frac{30}{10}=3\).

Step2: Check the included angle

The included angle \(\angle TAU=\angle BAC\) (common - sense assumption from the problem's context of comparing the two triangles for similarity, as the angle symbol is marked similarly for the two angles in the non - side - labeled part of the triangles).

Step3: Apply the similarity theorem

By the Side - Angle - Side (SAS) similarity theorem, if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the two triangles are similar.

Answer:

\(\triangle TAU\sim\triangle BAC\) by the Side - Angle - Side (SAS) similarity theorem.