Which geometric shape does not contain any perpendicular lines?

The geometric shape that does not contain any perpendicular lines is often a shape that can have all its angles that are not right angles or could have angles that are acute or obtuse. Among the given choices, a pentagon can be classified in such a way.

A pentagon is a five-sided polygon which can be irregular, meaning that the angles can vary widely and do not necessarily need to form any right angles. In contrast, a triangle can have right angles, a diamond (which is typically a rhombus) will often have perpendicular diagonals, and a rectangle consists exclusively of right angles. Therefore, while a pentagon may have angles that are not right angles, it does not need to have any perpendicular lines at all, making it the correct answer to the question.