Based only on the information given in the diagram, it is guaranteed that abc xyz

Statement is true.

Step-by-step explanation:

The given triangles ΔABC and ΔXYZ will be similar if the two angles of these triangles are equal Or all sides of both the triangles are equal Or two corresponding sides and the angle between these lines are same.

Here in ΔABC

∠ACB = 52°

∠ABC = 90°

Then we can find the third angle ∠CAB = 180°-(∠ACB+∠ABC)

                                                                 = 180 - (52+90)

                                                                 = 180 - 142

                                                                 = 38°

Similarly in ΔXYZ, ∠YXZ = 38°, ∠XYZ = 90°

Then ∠YZX = 180-(∠YXZ+∠XYZ)

                   = 180-(90+38) = 180-128 = 52°

Now we can say that in two triangles

∠ACB = ∠YZX =52°

∠CAB = ∠YXZ = 38°

Therefore These triangle are similar and the statement is true.

This statement is true