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It's not quite clear what's your question is actually asking but in general squares and rectangles consist of parallel and perpendicular line whereas right angle triangles have only perpendicular lines which meet at 90 degrees.

Q: What are three groups a shape could be In based on parallel and perpendicular lines?

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It could be a trapezoid

They could be: parallel lines, perpendicular lines or intersecting lines

Not necessarily. It could be a pentagonal based pyramid.

It could be a right angle triangle

It could be a square or a rectangle

Related questions

If you are sitting in a room, the ceiling and the floor are parallel to each other. The walls are perpendicular to the floor and to the ceiling. So any line on these surfaces will be parallel to or perpendicular to any line on the other surface. And if they were not, the building could be quite unstable.

It could be a trapezoid

They could be: parallel lines, perpendicular lines or intersecting lines

Parallelogram and a rectangle

Two lines are said to be parallel if perpendicular distance between them is always constant. Length of a pair of parallel lines need not to be same. It can be different.

If the field lines were not perpendicular to the surface, then they could be decomposed into components perpendicular and parallel to the surface. But if there is an E-field along the surface, the surface is no longer an equipotential.

Not necessarily. It could be a pentagonal based pyramid.

A circle.

It could be a right angle triangle

Parallelogram and a rectangle

It could be a square or a rectangle

The only requirement for a trapezoid is that one pair of opposite sides be parallel. There could be trapezoids with a pair of perpendicular lines.