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GATE 2021 CH – Question 2

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

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 is an indented chevron, B a triangle, C a square, and D a trapezium.
  1. Option A in the figure
  2. Option B in the figure
  3. Option C in the figure
  4. Option D in the figure

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Show answer and explanation

Correct answer: (A) Option A in the figure

Explanation

A convex polygon has no inward corner: every interior angle is at most 180 degrees. Option A has an inward notch, giving a reflex angle. A segment joining suitable points on opposite arms of the chevron passes outside the polygon.

The triangle, square and trapezium in B, C and D have no such indentation and are convex. **Answer: A.**