Question

A polygon is convex if, for every pair of points inside the polygon, the line segment joining them lies completely inside or on the polygon. Which one of the following is NOT a convex polygon? 

• A. A
• B. B
• C. C
• D. D

Hint:

Any polygon with a 'dent' or inward angle greater than \(180^\circ\) is automatically non-convex.

Answer 1

The Correct Option is A

A polygon is convex if, for every pair of points inside the polygon, the line segment joining them lies completely inside or on the polygon. This question asks us to identify which one of the given options is NOT a convex polygon.

1. Let's analyze the given options:
   1. The first shape (A) appears to have an indentation, implying that it's not a convex polygon. If you draw a line segment between certain internal points, the segment might go outside the boundary of the polygon.
   2. The second shape (B) is a triangle. Triangles are always convex because any line segment between two points inside will always stay within or on the boundary of the polygon.
   3. The third shape (C) is a rectangle. Similar to a triangle, any segment joining two points inside a rectangle will stay on or within the rectangle.
   4. The fourth shape (D) is a trapezoid. This doesn't have any indentations and is therefore convex, as all segments joining internal points remain within its boundary.
2. Since a convex polygon requires that for any two points inside the polygon, the line segment connecting them lies entirely inside the polygon, option (A) fails this test due to the indentation....
3. Therefore, the answer is Option A. It is the only shape that is not convex.