In triangle abc the measure of angle a is 35 and the measure of angle b is 20. in triangle def, the measure of angle d is 35 and the measure of angle f is 125. Are triangle abc and def similar? Explain or show reasoning.

Answer 1

No, the triangles are not similar. Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional. While angle a in triangle abc is congruent to angle d in triangle def, angle b in triangle abc does not have a corresponding congruent angle in triangle def. Therefore, the corresponding angles are not congruent, and the triangles cannot be similar.