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Convex or Concave Polygon

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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

  1. Look at each vertex. Check whether any corner bends inward.
  2. Check the angles. If one interior angle is reflex, meaning greater than 180°, the polygon is concave.
  3. 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.
  4. 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.

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