a Quadrilateral
"...need to be the same SIZE?" Quadrilateral (including trapezium).
An isosceles trapezoid has 2 sides that are the same length.
A trapezoid.
a prism
A polygon with two equal sides!
A three-sided polygon is called a triangle. If two of the sides are of the same length, it is said to be an isosceles triangle.
There are infinitely many such shapes. A polygon with 4 or more sides can have two sides that are parallel and they need not be the same length.
All the sides of a regular polygon have the same length. If two or more sides of a polygon have different lengths, then the polygon is not regular.
A regular polygon requires all sides to be the same length; in a rectangle not all four sides are the same length (they form two pairs of sides of equal length) and so it is not a regular polygon.
rectangle
The polygon you are describing is an isosceles triangle. An isosceles triangle has two sides that are of equal length, while the third side can be of a different length. This type of triangle also has two angles that are equal, corresponding to the two sides of the same length.
Every polygon has two of its sides intersect.