Identify the type of polygon
A convex polygon has all its interior angles smaller than 180°, so every diagonal stays inside the figure. A concave polygon has at least one interior angle greater than 180°, which creates an inward “dent.”
How to decide
- Look at each vertex. Check whether any corner bends inward.
- Check the angles. If one interior angle is reflex, meaning greater than 180°, the polygon is concave.
- Use diagonals as a visual test. If you can draw a segment between two vertices and part of it lies outside the polygon, the polygon is concave.
- If none of these signs appear and all corners point outward, the polygon is convex.
A reliable strategy
- Trace the shape carefully.
- Start with the most “inward” corner, if there is one.
- Compare the shape to a simple outward-bulging polygon such as a triangle or square.
Check your answer
Make sure your choice matches the shape’s geometry:
- Convex: no inward indentation, all interior angles less than 180°.
- Concave: at least one inward indentation, at least one interior angle greater than 180°.
If the exercise asks for a final answer, give the polygon type clearly and simplify any written response to just the correct classification.