Questions: If angle H and angle P each equal 38 degrees and angle G and angle Q each equal 41 degrees, is triangle F H G similar to triangle P R Q?

If $\angle H$ and $\angle P$ each equal 38 degrees and $\angle G$ and $\angle Q$ each equal 41 degrees, is $\triangle F H G \sim \triangle P R Q$ ? In $\triangle FHG$, we have $\angle H = 38^\circ$ and $\angle G = 41^\circ$. $\angle F + \angle H + \angle G = 180^\circ$ (sum of angles in a triangle). $\angle F + 38^\circ + 41^\circ = 180^\circ$ $\angle F + 79^\circ = 180^\circ$ $\angle F = 180^\circ - 79^\circ$ $\angle F = 101^\circ$ In $\triangle PRQ$, we have $\angle P = 38^\circ$ and $\angle Q = 41^\circ$. $\angle P + \angle Q + \angle R = 180^\circ$ (sum of angles in a triangle). $38^\circ + 41^\circ + \angle R = 180^\circ$ $79^\circ + \angle R = 180^\circ$ $\angle R = 180^\circ - 79^\circ$ $\angle R = 101^\circ$ Compare the angles of the two triangles. We have $\angle F = 101^\circ$, $\angle H = 38^\circ$, $\angle G = 41^\circ$. Also, $\angle R = 101^\circ$, $\angle P = 38^\circ$, $\angle Q = 41^\circ$. So, $\angle F = \angle R$, $\angle H = \angle P$, and $\angle G = \angle Q$. Determine if the triangles are similar. Since the corresponding angles of the two triangles are congruent, the two triangles are similar by the AA Similarity Theorem.

$\boxed{\text{yes because of the AA Similarity Theorem}}$

$\boxed{\text{yes because of the AA Similarity Theorem}}$