Question

are the triangles similar? if so, why? 18) △abc∼ a) not similar b) similar; aa similarity; △tas c) similar; sas similarity; △tas d) similar; sss similarity; △tas

Explanation:

Step1: Check for vertical angles

$\angle BAC$ and $\angle TAS$ are vertical angles. So, $\angle BAC=\angle TAS$.

Step2: Use AA similarity criterion

We are given $\angle B=\angle T$. By the AA (Angle - Angle) similarity criterion, if two angles of one triangle are equal to two angles of another triangle, the triangles are similar. So, $\triangle ABC\sim\triangle TAS$.

Answer:

B. similar; AA similarity; $\triangle TAS$