That is simply not true.
An isosceles trapezium, which is an isosceles triangle with its odd vertex chopped off by a line parallel to its base will have its non-parallel sides congruent.
Also, there is nothing to prevent one (or both) of the sloping sides being congruent to one of the parallel sides.
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A trapezoid, in general, does not have congruent sides.
Opposites sides of an isosceles trapezoid are congruent
A trapezoid may have zero or one pair of congruent sides.
Yes the non parallel sides of an isosceles trapezoid are congruent
A trapezoid normally has no congruent sides