We are told that all the segments from X to each vertex are congruent, and also all the angles at X have the same measure. Then, let's mark them all in the given diagram.
Now let's take a close look at △ ABX and △ DCX.
ccc
BX ≅ CX & & Side
∠ BXA ≅ ∠ CXD & & Included angle
XA ≅ XD & & Side
We can use the Side-Angle-Side (SAS) Postulate to conclude that △ BXA ≅ △ CXD, which is equivalent to say that △ ABX ≅ △ DCX.
