In ABC, ifAD is a median, then show thatAB +AC2 2(AD+BD?)ä¸ĺĽ9

1.	In ABC, ifAD is a median, then show thatAB +AC2 2(AD+BD?)ä¸ĺĽ9.ED
Answer» in triangle ABC, AD is median then , BD = BC in triangles ABD and ADC AB^2= AD^2+ BD^2 .........(1) AC^2= AD^2+ BC^2 ............(2) now add both the equations, AB^2+ AC^2= AD^2+ AD^2+ BD^2+ BC^2 AB^2+ AC^2= 2AD^2+ 2BD^2 [ since BD = BC] AB^2+ AC^2= 2[AD^2+ BD^2] hence proved.

In ABC, ifAD is a median, then show thatAB +AC2 2(AD+BD?)ä¸ĺĽ9.ED

Answer»

in triangle ABC, AD is median

then , BD = BC

in triangles ABD and ADC

AB^2= AD^2+ BD^2 .........(1)

AC^2= AD^2+ BC^2 ............(2)

now add both the equations,

AB^2+ AC^2= AD^2+ AD^2+ BD^2+ BC^2

AB^2+ AC^2= 2AD^2+ 2BD^2 [ since BD = BC]

AB^2+ AC^2= 2[AD^2+ BD^2]

hence proved.