Convex Polygon: Identifying the Convex Polygon

The following polygons are given:
1. Triangle ABC
2. Pentagon LMNOP
3. Hexagon XYZUVW

Definition of Convex Polygon:
A convex polygon is a polygon in which all line segments connecting any two points within the polygon lie inside the polygon. In simpler terms, a convex polygon does not have any indentations or "dents" in its shape.

Identifying the Convex Polygon:
To determine which of the given polygons is a convex polygon, we need to analyze each polygon individually.

Triangle ABC:
- A triangle is a 3-sided polygon.
- In triangle ABC, any line segment connecting two points within the triangle will always lie inside the triangle.
- Therefore, triangle ABC is a convex polygon.

Pentagon LMNOP:
- A pentagon is a 5-sided polygon.
- In pentagon LMNOP, there are line segments that can be drawn connecting points within the polygon that lie outside the shape.
- This indicates that pentagon LMNOP is not a convex polygon.

Hexagon XYZUVW:
- A hexagon is a 6-sided polygon.
- In hexagon XYZUVW, there are line segments that can be drawn connecting points within the polygon that lie outside the shape.
- This shows that hexagon XYZUVW is also not a convex polygon.

Conclusion:
- Among the given polygons, only triangle ABC is a convex polygon as all line segments connecting any two points within the triangle lie inside the triangle.

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