Question

are these triangles similar?
options: yes, no

Explanation:

Step1: Identify corresponding angles

In $\triangle FGH$, marked angles are $\angle G$ and $\angle H$. In $\triangle RST$, marked angles are $\angle S$ and $\angle R$.

Step2: Apply AA similarity rule

If two pairs of corresponding angles of two triangles are congruent, the triangles are similar. Here, $\angle G \cong \angle S$ and $\angle H \cong \angle R$, so the third pair of angles ($\angle F$ and $\angle T$) must also be congruent.

Step3: Conclude similarity

By the Angle-Angle (AA) Similarity Criterion, $\triangle FGH \sim \triangle TRS$.

Answer:

yes