How to prove mid point theorem
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triangle midpoint theorem :- the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and congruent to one half of the third side . here"s the proof below
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Mid point Theorem :
The line segment joining the mid points of any two sides of a triangle is parallel to the third side.
Given :
A \triangle ABC△ABC in which D and E are the mid points of AB and AC, respectively.
To prove :
DE \parallel BCDE∥BC.
Proof :
Since D and E are the mid points of AB and AC, respectively, we have AD=DBAD=DB and AE=ECAE=EC.
Therefore,
\dfrac{AD}{DB}=\dfrac{AE}{EC}
DB
AD
=
EC
AE
( each equal to 1 )
Therefore, by the converse of thales theorem, DE \parallel BCDE∥BC.
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