Question

how to prove midpoint theorem in practical file

Answer 1

Triangle Midpoint Theorem. Theorem: The line segment connecting themidpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.
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Answer 2

Given that:- A triangle ABC in which points E and F are mid points of sides AB & AC respectively.
To prove:- EF||BC and EF=1/2BC
Construction:- Through the vertex C of Triangle ABC, draw a line parallel to side BA which meets EF produced at point D.
PROOF:-
In triangle AEF & CDF
ang BAC=FCD( alternative interior angles)
AF=CF(F is mid points of AC)
AFE=CFD( vertically opp angles)
Triangle AEF congruent triangle CDF(by ASA criteria)
AE=CD & EF=DF___(1)
but AE=BE___(2)
BE=CD___(3)
now, BA||CD
BE||CD
BA||CD and BE||CD
Quadrilateral EBCD is a parallelogram.
ED||BC & ED=BC
EF||BC
But EF=DF
EF=1/2ED
EF=1/2BC
hence proved.


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