Final answer:
Triangle ABC is not similar to triangle DEF because they do not have the necessary two pairs of corresponding congruent angles; angle B in triangle ABC is not congruent to angle F in triangle DEF.
Step-by-step explanation:
To determine if triangles ABC and DEF are similar, we can use the angle-angle (AA) similarity criterion, which states that two triangles are similar if they have two corresponding angles that are congruent. In triangle ABC, the measure of angle A is 44º and the measure of angle B is 56º. In triangle DEF, the measure of angle D is 44º and the measure of angle F is 80º.
Since angle A from triangle ABC equals angle D from triangle DEF (both are 44º), we have one pair of congruent angles. However, angle B from triangle ABC is 56º, which is not congruent to angle F from triangle DEF, which is 80º. To have similar triangles, we need both the corresponding angles to be congruent.
Therefore, triangle ABC is not similar to triangle DEF because they do not have two pairs of corresponding angles that are congruent. This satisfies the AA similarity criterion which requires two pairs of corresponding congruent angles. Without this, we cannot establish similarity between the two triangles.