Question 952394
your proof is based on the properties of a kite.
<a href = "http://www.coolmath.com/reference/kites.html" target = "_blank">http://www.coolmath.com/reference/kites.html</a>


if you stand the kite up along the long diagonal, the horizontal anbles opposite to each other are congruen.
the short sides above the horizontal are congruent.
the long sides under the horizontal are congruent.
the long diagonal splits the kite into 2 goncguent triangle by SAS.
there is no additional construction needed as the properties of the kite itself provide the proof based on the properties of the kite.
check out the reference and  you'll see what i mean.