We can get noncongruent trapezoids with congruent diagonals if we translate a diagonal of a trapezoid parallel to the bases.
Let's copy two of these trapezoids to answer the question.
By construction, these are trapezoids and the corresponding diagonals are congruent.
The trapezoids are not congruent because neither the sides nor the angles are congruent.
Alternative Solution
Alternative Way of Thinking
A different method of drawing noncongruent trapezoids with congruent diagonals is to rotate one diagonal around the intersection point of the diagonals.
It can be shown that using this rotation the bases remain parallel.
The concept of similar triangles is needed to complete a proof.
You will learn about this a bit later.
