Home
Class 10
MATHS
Seg AD is the median of triangleABC and ...

Seg AD is the median of `triangleABC` and `AM_|_BC`. Prove that : `(i) AC^2=AD^2+BCxxDM+((BC)/2)^2` `(ii) AB^2=AD^2-BCxxDM+((BC)/2)^2`.

Text Solution

Verified by Experts

`1)In/_AMC`
`AC^2=AM^2+MC^2-(1)`
`In/_AMD`
`AD^2=AM^2+MD^2`
`AM^2=AD^2-DM^2-(2)`
`AC^2=AD^2-DM^2+MC^2`
`AC^2=AD^2+((BC)/2)^2+2*DM*(BC)/2`
`AC^2=AD^2+DM*BC+((BC)/2)^2`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

In Fig.6.60, AD is a median of a triangle ABC and AM_|_BC .Prove that :(i) AC^2=AD^2+BC.DM+((BC)/2)^2

In Fig.6.60, AD is a median of a triangle ABC and AM_|_BC .Prove that :(ii) AB^2=AD^2-BC.DM+((BC)/2)^2

In fig., AD is a median of a triangle ABC and AM bot BC.Prove that :- AC^2=AD^2+BC.DM+((BC)/2)^2 . .

In fig., AD is a median of a triangle ABC and AM bot BC.Prove that :- AB^2=AD^2-BC.DM+((BC)/2)^2 . .

In Fig . AD is a median of a triangle ABD and AM bot BC. Prove that : AC^(2)=AD^(2)+BC. DM+((BC)/(2))^(2)

In Fig . AD is a median of a triangle ABD and AM bot BC. Prove that : AB^(2)=AD^(2)-BC.DM+((BC)/(2))^(2)

In Fig.6.60, AD is a median of a triangle ABC and AM_|_BC .Prove that :(iii) AC^2+AB^2=2AD^2+1/2BC^2

In Delta ABC , AD is a median and AM _|_ BC.Prove that (a) AC^(2) = AD^(2) +BC.DM+ ((BC)/(2))^(2) (b) AB^(2) = AD^(2) -BC.DM+ ((BC)/(2))^(2) (c ) AC^(2) + AB^(2) = 2AD^(2) +(1)/(2) BC^(2)

AD is a median of triangle ABC. Prove that : AB+BC+AC gt 2AD