State if the statement “In a triangle, the sum of the squares of any two sides is equal to twice the square of the median which bisect the third side” is true or false.

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True

False

answer is B.

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Detailed Solution

It is given that “In a triangle, the sum of the squares of any two sides is equal to twice the square of the median which bisect the third side”.
Hence, using the Pythagoras theorem.

Δ A B E A B 2 = A E 2 + B E 2 Δ A E C A C 2 = A E 2 + E C 2

Adding both the equations.

Δ A B C ≈ Δ Q R P

A B 2 + A C 2 = 2 A D 2 + 2 12 B C 2 B C = 2 B D

Hence, the sum of squares of any two sides is equal to twice the square of the median which bisects the third side. Therefore, option 2 is correct.

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