What is a polygon with opposite sides paralle and congruent called?

Answer 1

That depends somewhat on other characteristics of the polygon.

-- If it has four sides and one pair of them is parallel and congruent, then the
other pair must also be parallel and congruent, and it's called a parallelogram.

-- If it has four sides, parallel and congruent opposite sides, and a right angle,
then it's called a rectangle.

-- If it has four sides and all four sides are congruent, then opposite sides must be
parallel, and it's called a rhombus.

-- If it has four sides and both pairs of sides are parallel and all four are congruent
and it has a right angle, then it's called a square as well as a rhombus.

-- Any polygon with more than four sides can have at least one pair of opposite
parallel congruent sides and possibly more, but doesn't necessarily have.

-- If it's a regular polygon, then it has one or more such pairs of sides if, and only if,
it has an even number of sides.

-- In any case with more than four sides, the polygon is named for its number of sides.

And I believe that pretty well covers it.