Concave and convexConvex - A shape or surface that curves or bulges outward. In geometry, a convex shape is one where any line segment drawn between two points on the shape lies entirely within the shape.Concave - A shape or surface that curves inward, creating a hollow or recessed area. In geometry, a concave shape has at least one line segment that can be drawn between two points on the shape that passes outside of the shape.