A pentagonal prism
One shape is the [quadrilateral] pyramid. Since this is a self-dual polyhedron, I cannot see what the other shape could be.
The shape you've described is a right pentagonal prism.
A right angled triangle is an example of a shape with exactly 2 perpendicular sides.
A right pentagonal prism.
A shape that has 2 parallel lines and 4 perpendicular lines is a rectangle. In a rectangle, the opposite sides are parallel, while the adjacent sides are perpendicular to each other. Therefore, a rectangle fits the description of having two sets of parallel lines and four right angles formed by the perpendicular lines.
trapezoid
A parallelogram.
A shape that has two parallel lines and no perpendicular lines is a trapezoid, specifically an isosceles trapezoid. In this shape, one pair of opposite sides is parallel, while the other pair is not perpendicular to the parallel sides. This creates a unique geometry without right angles. Another example could be a parallelogram, which also has two pairs of parallel sides but does not necessarily have any perpendicular lines.
parallelogram
X and T because the they can still make the T shape and still be perpendicular
a squareof course
A right angled triangle.