PRESENTATION TO PROVE -

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

.

given :-in the given figure e and f are the mid

points of side ab and ac respectively and cd||ba

To prove :-• The line segment joining

the mid points of two sides of a triangle is parallel to the third side.

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)

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)

THANK U