4. Given $\triangle A B C$ is an isosceles right triangle, $\angle C$ $=90^{\circ}, D 、 E$ are two points on side $A B$, and point $D$ is between $A E$, $\angle D C E=45^{\circ}$. Then the triangle formed by $A D 、 D E 、 E B$ as side lengths is ( ).
(A) acute triangle
(B) obtuse triangle
(C) right triangle
(D) cannot be determined
4.C.

Rotate $\triangle C A D$ counterclockwise by $90^{\circ}$ around point $C$, to get $\triangle C B F$, then
$$
B F=A D, \angle E B F=90^{\circ} \text {. }
$$

Since $\triangle C D E \cong \triangle C F E$, we have $E F=D E$.
Thus, $A D^{2}+E B^{2}=D E^{2}$.
Therefore, the triangle formed by the side lengths $A D, D E, E B$ is a right triangle.