Q.2 A polygon is convex if, for every pair of points, P and Q belonging to the
polygon, the line segment PQ lies completely inside or on the polygon.
Which one of the following is NOT a convex polygon?

📘 Introduction

In geometry, polygons are classified as convex or concave based on their shape.
A convex polygon has no inward dent—meaning for any two interior points you choose, the line segment joining them lies completely inside the shape.
This concept frequently appears in competitive exams.
Let’s analyze the given options to find which one is NOT a convex polygon.

❓ Problem Statement

A polygon is convex if, for every pair of points $P$ and $Q$ inside the polygon, the line segment $PQ$ lies completely inside or on the polygon.

Which one of the following is NOT a convex polygon?

Options provided: A, B, C, D

🔍 Explanation of Each Option

✔️ Option (A)

This polygon has an indentation or inward notch, making one of its internal angles greater than 180°.
A line joining certain points inside this shape will pass outside the boundary.

➡️ Therefore, Option (A) is NOT a convex polygon — it is concave.

✔️ Option (B)

The figure here is a triangle.
All triangles are always convex, as every interior angle is less than 180°.

➡️ Option (B) is convex.

✔️ Option (C)

This shape is a rectangle or quadrilateral with straight outward edges.
No inward bend exists.

➡️ Option (C) is convex.

✔️ Option (D)

This figure is a trapezoid or quadrilateral with no inward indentation.
All edges bulge outward, and internal angles are less than 180°.

➡️ Option (D) is convex.

🎯 Correct Answer

⭐ Option (A) is NOT a convex polygon.

It contains a dent that makes part of the interior open outward, classifying it as concave.

🏁 Conclusion

To identify a non-convex polygon, simply check whether the shape has a dent or if any interior angle exceeds 180°.
Among the given shapes, only Option (A) fails this convexity test.