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Centroid

Prove that th...

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Prove that the centroid of any triangle is same as the centroid of the new triangle formed by joining the mid point of its sides

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Q. Assertion :If

(0, 3)

(2, 2)

(- 2, 1)

be the mid points of the sides of a triangle, then centroid of the original triangle is

(0, 2)

. Reason: Centroid of the original triangle & triangle obtained by joining the mid points of the sides of the triangle is (unaltered) same.

State true or false

Using vector method the centroid of the triangle formed by joining the mid points of the sides of a given triangle coincides with the centroid of the given triangle.

(- 2, 3), (4, - 3), (4, 5)

are mid-points of the sides of a triangle, find the coordinates of the centroid of the triangle formed by these mid-points.

Q. Prove that the line joining the mid-point of any two sides of a triangle is parallel to the third side.

Q. Prove that the four triangles formed by joining in pairs, the mid-points of three sides of a triangle, are congruent to each other.

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