Question

14 multiple choice 1 point are the following triangles similar, if so, state the similarity criterion. (image of triangles) options: yes, sas; no, the triangles are not similar; yes, aa; yes, sss

Explanation:

Step1: Identify Vertical Angles

Vertical angles are equal. $\angle SEG$ and $\angle RES$ (wait, actually $\angle FEG$ and $\angle SER$? Wait, looking at the diagram, $\angle FEG$ and $\angle SER$ are vertical angles, so they are equal. Also, $\angle F$ and $\angle R$ are right angles? Wait, the marks: $F$ and $R$ have right angle marks? Wait, the diagram shows $FR$ and $SR$? Wait, maybe $\angle F$ and $\angle R$ are right angles (90 degrees), so they are equal. Then we have two angles: one pair of vertical angles (equal) and one pair of right angles (equal). So by AA (Angle - Angle) similarity criterion, the triangles are similar.

Step2: Apply AA Similarity

AA similarity states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar. Here, we have one pair of vertical angles (equal) and one pair of right angles (equal), so two angles are equal. Thus, the triangles are similar by AA.

Answer:

Yes, AA (The correct option is the one with "Yes, AA")