Question

show that incentre, orthocentre, circumcentre and centroid meet at the same point in an equilateral triangle name the point​

Answer 1

Answer:

It’s easy. In a symmetric triangle, the triangle centers can’t change when we map the triangle to itself using the symmetry. The symmetry mapping has to preserve the triangle centers.

So in an isosceles triangle, with bilateral symmetry, all the triangle centers must be on the line of symmetry, because the points on the line are the only fixed points when we map the triangle to its symmetric self.

An equilateral triangle has rotational symmetry around the centroid. If we rotate an equilateral triangle 120∘ around the centroid, it ends up the same — that’s the symmetry. The only point left unchanged by the rotation is the center of rotation, the centroid. That centroid must be all the triangle centers of the equilateral triangle, since it’s the only point that’s fixed under the symmetry.

Step-by-step explanation:

hope it helps you ☺️

Answer 2

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