Question

what is mid-point theorm??? and formula ​

Answer 1

Answer:

Mid-Point Theorem :-

The line segment joining the mid-points of two sides of a triangle is parallel to the third side and equal to half of the third side.

Answer 2

THE LINE SEGMENT JOINING THE MID POINTS OF ANY TWO SIDES OF AN TRIANGLE IS PARALLEL TO THE THIRD SIDE AND EQUAL OF HALF OF IT

GIVEN
In ABC,E and F are the mid points of AB and AC.
TO PROVE
EF || BC and EF = 1/2
CONSTRUCTION
Through vertex C, draw CD || BA and let it meets extended EF at D.
PROOF
In AEF and CDF
angle AEF = angle CFD ( Vertically opposite angle )
AF = FC ( F is the mid-point of AC )
angle EAF = angle FCD ( Alternative interior angle )
By ASA,
AEF is congruent toCDF
Thus,
AE = CD and EF = FD ( by C.P.C.T. )-------( 1 )
also,
AE = BE ( E is the mid-point of AB )----------(2)
From equation ( 1 ) and (2),
AE = BE = CD
and
BE || CD ( by construction )
so,
BCDE is a ||gm [ because one pair of opposite sides is parallel and equal ]
then,
ED || BC
or,
EF || BC
and ED = BC
now,
=> BC = ED = EF + FD
= EF + EF [ from equation ( 1 ) EF = FD ]
=> EF = 1/2 BC

PROVED
hope it helps uh

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