Question

are these triangles similar? s t r 54° 94° f g h 49° 94° yes no write a similarity statement. △ ~ △

Explanation:

Step1: Find the third - angle of each triangle

In $\triangle SRT$, using the angle - sum property of a triangle ($180^{\circ}$), the third angle $\angle S=180^{\circ}-(94^{\circ} + 54^{\circ})=32^{\circ}$. In $\triangle FGH$, the third angle $\angle H=180^{\circ}-(94^{\circ}+49^{\circ}) = 37^{\circ}$. But we can also use the AA (angle - angle) similarity criterion. We see that $\angle R=\angle F = 94^{\circ}$. Also, we know that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Step2: Write the similarity statement

We match the corresponding angles. $\angle R$ corresponds to $\angle F$, $\angle T$ corresponds to $\angle G$, and $\angle S$ corresponds to $\angle H$. So the similarity statement is $\triangle SRT\sim\triangle FHG$.

Answer:

yes
$\triangle SRT\sim\triangle FHG$