In right-angled triangle `A B C` in which `/_C=90^@` , if `D` is the mid-point of `B C` , prove that `A B^2=4\ A D^2-3\ A C^2` .

In a right ABC right-angled at C, if D is the mid-point of BC, prove that BC^(2)=4(AD^(2)-AC^(2))

In Delta ABC, angle B = 90^(@) and d is the mid - point of BC. Prove that AC ^(2) = AD^(2) + 3CD ^(2)

In A B C , A D is a median. Prove that A B^2+A C^2=2\ A D^2+2\ D C^2 .

In Fig.3,ABC is a right triangle,right angled at C and D is the mid-point of BC.Prove that AB^(2)=4AD^(2)-3AC^(2)

If D is the mid-point of the hypotenuse A C of a right triangle A B C , prove that B D=1/2A C . GIVEN : A A B C in which /_B=90^0 and D is the mid-point of A Cdot TO PROVE : B D=1/2A C CONSTRUCTION Produce B D to E so that B D=D Edot Join E Cdot

If in a triangle ABC, the altitude AM be the bisector of /_BAD , where D is the mid point of side BC, then prove that (b^2-c^2)= (a^2)/(2) .

If A D is a median of a triangle A B C ,\ then prove that triangles A D B\ a n d\ A D C are equal in area. If G is the mid-point of median A D , prove that a r\ ( B G C)=2a r\ (\ A G C)

If in a triangle ABC ,the altitude AM be the bisector of /_BAD, where D is the mid point of side BC, then prove that (b^(2)-c^(2))=a^(2)/2

In figure, ABC is a triangle in which /_A B C=90^@ and A D_|_B C . Prove that A C^2=A B^2+B C^2-2B C.B D .

A B C is a triangle in which D is the mid-point of B C and E is the mid-point of A Ddot Prove that area of B E D=1/4a r e aof A B Cdot GIVEN : A A B C ,D is the mid-point of B C and E is the mid-point of the median A Ddot TO PROVE : a r( B E D)=1/4a r( A B C)dot