Question

prove
that
three
times the
sum of the
of the squares of a
triangle is equal to four times the sum of
of squares of the
medians
of
that
triangle​

Answer 1

Answer:

Yeah its true..

Step-by-step explanation:

Follow the inserted solution....

Answer 2

Answer:

Appollonius theorem states that the sum of the squares of the two sides is equal to twice the square of the median on the third side plus half the square of the third side

hence,AB2+AC2 =2BD2+2AD2

=2×(1/2BC)2+2AD2

=1/2BC2  +2AD2

∴2AB2+2AC2=BC2+4AD2→1

SIMILARLY we get

2AB2+2BC2=AC2+4BE2→2

2BC2+2AC2=AB2+4CF2→3

ADDING (1)(2)AND(3),WE GET

4AB2+4BC2+4AC2=AB2+BC2+AC2+4AD2+4BE2+CF2

3(AB2+BC2+AC2)=4(AD2+BE2+CF2)

HENCE,THAT THREE TIMES THE SUM OF THE SQUARES OF THE TRIANGLE IS EQUAL TO FOUR TIMES THE SUM OF SQUARES OF THE MEDIANS OF THAT TRIANGLE.