are these triangles similar?\nwrite a similarity statement.\n△ ~ △

Explanation:

Step1: Find the third angle of triangle ( \triangle DEF )

The sum of angles in a triangle is ( 180^{\circ} ). Let the third angle be ( \angle F ). [ \begin{align*} \angle F&=180^{\circ}-(31^{\circ} + 58^{\circ})\ &=180^{\circ}-89^{\circ}\ &=91^{\circ} \end{align*} ]

Step2: Check the correspondence of angles

In ( \triangle DEF ), angles are ( 31^{\circ},58^{\circ},91^{\circ} ). In ( \triangle VWU ), angles are ( 31^{\circ},58^{\circ},91^{\circ} ) (since ( \angle V = 58^{\circ},\angle W=31^{\circ} ), and ( \angle U=180^{\circ}-(31^{\circ}+58^{\circ}) = 91^{\circ} )).

Step3: Write the similarity statement

Corresponding angles are equal. So, ( \triangle DEF\sim\triangle VWU )

Answer:

( \triangle DEF\sim\triangle VWU )