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? A. (arrow/chevron shape pointing right) B. (equilateral triangle) C. (rectangle) D. (trapezoid)

GATE 2021 · General Aptitude · Patterns In Two Dimensions · medium

Answer: Option A (arrow/chevron shape) is NOT a convex polygon because its notch creates reflex angles and a segment between certain boundary points exits the shape.

1. Check option B: equilateral triangle: A triangle is always convex — no reflex angles possible. Segment between any two boundary points stays inside.
2. Check option C: rectangle: A rectangle is a standard convex polygon — all right angles, no concavities.
3. Check option D: trapezoid: A convex trapezoid has all interior angles less than 180°. Any two boundary points connect inside the shape.
4. Check option A: arrow/chevron shape: The concave notch at the tail of the arrow creates reflex angles. A line segment drawn between the two outer tail-tips passes through the empty notch space — entirely outside the polygon boundary. This violates the convexity definition.