Many shapes. If it is a triangle, it is an isosceles triangle. A quadrilateral (4 sides) may be several types depending on other conditions. Just a quadrilateral (adjacent sides congruent and no other special condition) a parallelogram, a rhombus, a square, and a rectangle (all are quadrilaterals). But there is nothing that says a pentagon, hexagon, etc. cannot have t congruent sides.
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Yes, all trapezoids must have one pair of congruent sides.
I think a trapezoid.
No. Most trapezoids don't even have one pair of congruent sides. Only isosceles trapeoids have one pair; none have more than one pair.
A trapezoid may have zero or one pair of congruent sides.