In general, you cannot tell. For example, try it with a near-regular hexagon.
cut out the polygon and fold the two sides onto each other.if the sides match up, you can assume its congruent
This shape would be a square.
A trapezium with all its sides congruent is an impossible shape.
This is a parallelogram. The first requirement is 2 pairs of congruent sides where the congruent sides are not adjacent. This is like a rectangle (excluding a square) that has two pairs of congruent sides where the congruent sides are not adjacent. But the angles are not all congruent (as set in the question) which pushes the shape into the "next less regular" shape, the parallelogram. The angles will not all be congruent, but it will have 2 pairs of congruent angles. There is no way to avoid the 2 pairs of congruent angles because of the requirement that the shape must have 2 pairs of congruent sides (the first requirement).
If a triangle does not have the same length side as another triangle the sides are not congruent.
cut out the polygon and fold the two sides onto each other.if the sides match up, you can assume its congruent
That is a mathematical impossibility. At least 2 angles have to be congruent in order for the shape to have 4 sides.
Angles and sides are congruent when they are identical. A shape with four identical sides and angles is a square.
Congruent sides are two (or more) sides of a shape that have the same measure.
This shape would be a square.
A trapezium with all its sides congruent is an impossible shape.
This is a parallelogram. The first requirement is 2 pairs of congruent sides where the congruent sides are not adjacent. This is like a rectangle (excluding a square) that has two pairs of congruent sides where the congruent sides are not adjacent. But the angles are not all congruent (as set in the question) which pushes the shape into the "next less regular" shape, the parallelogram. The angles will not all be congruent, but it will have 2 pairs of congruent angles. There is no way to avoid the 2 pairs of congruent angles because of the requirement that the shape must have 2 pairs of congruent sides (the first requirement).
rectangle
If a triangle does not have the same length side as another triangle the sides are not congruent.
obtuse
a regular polygon
A rhombus