state and prove midpoint theorem
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"The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”
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State and prove mid point theorem.
December 26, 2019avatar
Anwar Kapane
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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 △ABC in which D and E are the mid points of AB and AC, respectively.
To prove :
DE∥BC.
Proof :
Since D and E are the mid points of AB and AC, respectively, we have AD=DB and AE=EC.
Therefore,
DB
AD
=
EC
AE
( each equal to 1 )
Therefore, by the converse of ∥BC.
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