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Question

The median of a triangle divides it into two triangles of equal areas. State True or False.

A

Statement 1 is true and Statement 2 is false.

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B

Both the statements are true and Statement 1 is a particular case of Statement 2.

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Solution

The correct option is A

Statement 1 is true and Statement 2 is false.


Median is the line segment joining a vertex of a triangle to the midpoint of the opposite side. Since the opposite side is bisected by the median, lengths of the base of the triangles into which the median divides the original triangle are the same. Also, the perpendicular distance to the opposite vertex remains the same. Since the area of a triangle only depends on base and height, areas of both the triangles will be the same.
Hence, the given statement is true.

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