mid point theorem
TRANSCRIPT
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PRESENTATION TO PROVE -
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THE MID POINT THEOREM
The mid point theorem state that
The line segment joining the mid points of two sides of a triangle is
parallel to the third side
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.
given :-in the given figure e and f are the mid
points of side ab and ac respectively and cd||ba
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To prove :-• The line segment joining
the mid points of two sides of a triangle is parallel to the third side.
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Proof:-In ∆AEF and ∆CDF
Angle EAF = CFD (alternative interior angle)
AF = FC (As F is the mid point of AC)
Angle AFC = DFC (vertically opposite angles)
.∙.∆AEF is congruent to ∆CDF (ASA criteria for congruence)
So, EF = DF (by CPCT)
And, BE = AE (Given)
Again, AE = DC (by CPCT)
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Therefore, BE = DC (that are opposite sides of BCDE)
As, the opposite sides of BCDE are equal ,therefore BCDE
is a parallelogram.
This gives EF||BC (As the sum of the adjacent angles of a parallelogram is 180˚)
(Hence Proved)
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