While both triangles have a right angle and an equal side length, without more information, we cannot definitively conclude that △ABC is congruent to △DEF. Additional details about other sides and angles are crucial for a conclusive decision.
The congruence of two triangles is determined by the congruence of their corresponding sides and angles. Given that (△ABC) has a right angle at (A) with (AB = 4) and (△DEF) has a right angle at (D) with (DE = 4), it's tempting to assume congruence. However, congruence is not necessarily guaranteed.
For congruence, all corresponding angles and sides must be equal. While both triangles share a right angle and have an equal side length (AB = DE = 4), it's essential to know more about the remaining sides and angles. The information provided is insufficient to conclude congruence. The length of (BC) and (AC) in (△ABC) and the length of (EF) and (DF) in △DEF is unknown.
Without additional information, we cannot assert that △ABC is congruent to △DEF. Additional details about the remaining elements of both triangles are required for a conclusive determination of congruence.
The question probable may be:
In △ABC, if m∠A = 90° and AB = 4, and in △DEF, m∠D = 90° and DE = 4, is it guaranteed that △ABC is congruent to △DEF? Provide a rationale for your response.