Question

are these triangles similar? yes no

Explanation:

Step1: Calculate the third angle of triangle \( VWU \)

The sum of angles in a triangle is \( 180^{\circ} \). Let the third angle of \( \triangle VWU \) be \( \angle W \).

$$ \angle W=180^{\circ}-(100^{\circ} + 30^{\circ})=50^{\circ} $$

Step2: Calculate the third angle of triangle \( QRS \)

Let the third angle of \( \triangle QRS \) be \( \angle R \).

$$ \angle R=180^{\circ}-(100^{\circ}+35^{\circ}) = 45^{\circ} $$

Step3: Check the AA (Angle - Angle) similarity criterion

For two triangles to be similar, their corresponding angles must be equal. In \( \triangle VWU \), angles are \( 100^{\circ},30^{\circ},50^{\circ} \) and in \( \triangle QRS \), angles are \( 100^{\circ},35^{\circ},45^{\circ} \). Since not all corresponding angles are equal.

Answer:

no