Question

The centre of a triangle must always be found inside the triangle. Illustrate the statement with examples or deny the statement using counter-examples. A diagram would be helpful in supporting your opinion

Answer 1

The center of a triangle must always be found inside the triangle given that it is concurrent point of the three median lines of the triangle all three of which are located only inside of the triangle

The examples of the properties of the center of a triangle are;

1. The center of the triangle is the centroid of the triangle which is the point of concurrency of the three medians of the triangle, where a median line is the line which connects a vertex to the midpoint of the side opposite the vertex inside the triangle
2. Each median line divides the area of the triangle in half, and given that the area of the triangle is equal to half the altitude, multiplied by the length of the base side of the triangle, the three medians of a triangle are related and share a common concurrent point inside the triangle such the perpendicular distance from the concurrent point of the three medians to each of the three side is less than the altitude of the triangle

Given that the three medians are located inside the triangle therefore, based on the location of the center of the triangle on the medians of the triangle, the center of the triangle must always be found inside the triangle

Learn more about the centroid of a triangle here;

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