Question

true or false: these triangles are similar. a true b false

Explanation:

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

The sum of angles in a triangle is \( 180^{\circ} \). For \( \triangle DEF \), if one angle is \( 105^{\circ} \) and \( \angle EDF=180 - 43=137^{\circ} \) (linear - pair), then the third angle \( \angle DFE=180-(105 + 37)=38^{\circ} \)

Step2: Check the angle - angle similarity criterion

For \( \triangle ABC \), angles are \( \angle A = 105^{\circ}\), \( \angle C=34^{\circ}\), so \( \angle B=180-(105 + 34)=41^{\circ}\)
Since the angles of \( \triangle ABC\) (\(105^{\circ},41^{\circ},34^{\circ}\)) and \( \triangle DEF\) (\(105^{\circ},37^{\circ},38^{\circ}\)) are not equal.

Answer:

B. False