Question

State and prove mid point theorem.​

Answer 1

Answer :

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

Take a triangle ABC , E and F are the mid points of side AB and AC respectively .

Construction : Through C , draw a line ll BA to meet EF produced at D .

Proof :

In triangle AEF and CDF

AF = CF ( F is the mid point )

LAFE = LCFD ( Alternate angle , BA ll CD )

Therefore , Triangle AEF = DCF ( ASA )

EF = FD and AE = CD ( CPCT ) ... (1)

AE = BE ( E is the mid point of AB ) ... (2)

BE = CD ( from eq. (1) (2) )

Therefore , EBCD is llgm.

( BA ll CD )

( BE = CD )

EF ll BC , ED = BC ( since EBCD Is llgm . )

EF = 1/2 ED ( Since EF = FD )

EF = 1/2 BC ( Since ED = BC )

HENCE , EF ll BC AND EF = 1/2 BC

BY MID POINT THEOREM .