Plz solve ....
In triangle ABC,D and E are mid points of sides BC and AC respectively. Find the length of DE.Prove the DE=1/2 AB?
Answers
Answered by
1
Lets use triangle similarity here
The traingle ABC and ADE are similar
Proof:
We know D is mid point of BC
So BD:BC = 1:2
We know E is mid point of AC
So AE:AC = 1:2
And angle DCE = BCA, (its just same)
So SAS similarity
As the triangles are similar
BD:BC = AE:AC = DE:AB = 1:2
So DE = 2 AB
The traingle ABC and ADE are similar
Proof:
We know D is mid point of BC
So BD:BC = 1:2
We know E is mid point of AC
So AE:AC = 1:2
And angle DCE = BCA, (its just same)
So SAS similarity
As the triangles are similar
BD:BC = AE:AC = DE:AB = 1:2
So DE = 2 AB
Kanikashah:
Thanks ..but what about the length of DE...?
it depends on AB
given AB i can get DE, I think its not possible to get actual length
with given data
Hmm I am also not getting the answer...
Answered by
0
This can be easily proved by converse of BPT theorem.
According to it a line drawn by joining the mid points of any two sides of a triamgle is parallel to third side and half of third side.
So hence in triangle ABC.,
DE=1÷2AB.
Hope you understand...... :)
According to it a line drawn by joining the mid points of any two sides of a triamgle is parallel to third side and half of third side.
So hence in triangle ABC.,
DE=1÷2AB.
Hope you understand...... :)
Similar questions