Question

are these triangles similar?
write a similarity statement.
△ ~ △

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 \( \angle F \).

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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:

\( \triangle DEF\sim\triangle VWU \)