Based on the information marked in the diagram, two triangles must be congruent.

1. Analyze the given information for triangle XYZ:
We are given that $\angle XZY$ is a right angle (indicated by the square symbol), so $\angle XZY = 90^\circ$. The tick marks on sides $XZ$ and $YZ$ indicate that $XZ = YZ$. This means triangle XYZ is an isosceles right triangle.

2. Analyze the given information for triangle ABC:
We are given that $\angle ACB$ is a right angle (indicated by the square symbol), so $\angle ACB = 90^\circ$. The double tick marks on sides $BC$ and $AB$ indicate that $BC = AB$. This means triangle ABC is an isosceles triangle, but it is not necessarily a right triangle at C. However, the diagram shows a right angle at C, implying $\angle ACB = 90^\circ$. The double tick marks on $BC$ and $AB$ are contradictory if $\angle ACB = 90^\circ$, as the hypotenuse ($AB$) must be longer than the legs ($BC$ and $AC$). Assuming the tick marks on $BC$ and $AC$ were intended to be equal, then $\triangle ABC$ would be an isosceles right triangle with $BC = AC$. If we strictly follow the diagram, the double tick marks on $BC$ and $AB$ imply $BC = AB$. In a right triangle, the hypotenuse is always the longest side, so $AB > BC$. Therefore, $BC = AB$ is only possible if $BC = AB = 0$, which is not a triangle. Let's assume there is a typo in the tick marks for $\triangle ABC$ and that the intention was to show $BC = AC$ to make it an isosceles right triangle, or that the double tick marks on $BC$ and $AB$ are correct and it is not an isosceles right triangle.

3. Compare the triangles for congruence:
For $\triangle XYZ$ to be congruent to $\triangle ABC$, we need to satisfy one of the congruence postulates (SSS, SAS, ASA, AAS, or HL for right triangles).

From $\triangle XYZ$, we have: $\angle XZY = 90^\circ$, $XZ = YZ$.

From $\triangle ABC$, we have: $\angle ACB = 90^\circ$, and $BC = AB$ (as marked, though this is geometrically impossible for a non-degenerate triangle).

Let's consider the case where the tick marks on $BC$ and $AC$ were intended to be equal, so $BC = AC$. In this case, $\triangle ABC$ is an isosceles right triangle with $\angle ACB = 90^\circ$ and $BC = AC$. We also have $XZ = YZ$ in $\triangle XYZ$. However, we do not have any information about the angles in $\triangle ABC$ or $\triangle XYZ$ other than the right angles, nor do we have information about the lengths of the hypotenuses ($XY$ and $AB$) or the other legs ($YZ$ and $AC$).

Even if we assume $\triangle ABC$ is an isosceles right triangle with $BC=AC$, we only know that $XZ=YZ$ and $BC=AC$. We do not know if $XZ = BC$ or $YZ = AC$. Therefore, we cannot conclude congruence.

If we strictly follow the diagram with $BC = AB$, this is an impossible triangle. However, if we interpret the double tick marks on $BC$ and $AB$ as a mistake and assume that the diagram intends to show some relationship, we still lack sufficient information.

Let's assume the question implies that $\triangle XYZ$ is an isosceles right triangle (which it is, based on $XZ=YZ$ and $\angle XZY = 90^\circ$) and $\triangle ABC$ is also an isosceles right triangle (which it would be if $BC=AC$ and $\angle ACB = 90^\circ$). Even in this scenario, we only have Angle-Leg-Leg (ALL) congruence, which is not a valid congruence postulate. We would need at least one more piece of information, such as $XZ = AC$ or $YZ = BC$ or $XY = AB$ or $\angle YXZ = \angle BAC$.

Given the markings, we have: $\angle XZY = 90^\circ$, $XZ = YZ$. And $\angle ACB = 90^\circ$, $BC = AB$. The condition $BC=AB$ in a right triangle is impossible. If we ignore this and assume it's a typo and meant $BC=AC$, then we have two isosceles right triangles. However, we do not have enough information to prove congruence. For example, $\triangle XYZ$ could be smaller than $\triangle ABC$.

Therefore, based on the information marked in the diagram, $\triangle XYZ$ and $\triangle ABC$ do not necessarily have to be congruent.