"Based only on the information given in the diagram, it is guaranteed that ΔABC ~ ΔDEF" is true.
The statement in the image is true.
Triangles ABC and DEF are similar by the AA Similarity Postulate. This postulate states that if two triangles have two corresponding angles that are congruent, then the triangles are similar. In the image, we see that angle A is congruent to angle D, and angle B is congruent to angle E. Therefore, triangles ABC and DEF must be similar.
Here's a more detailed explanation:
Angle A is congruent to angle D: Both angles are marked as right angles (90 degrees).
Angle B is congruent to angle E: Both angles are marked as 31 degrees.
Since triangles ABC and DEF have two pairs of congruent angles, they must be similar. This means that the corresponding side lengths of the triangles are proportional.
Therefore, the statement "Based only on the information given in the diagram, it is guaranteed that ΔABC ~ ΔDEF" is true.