Question

explain mid point theorem........​

Answer 1

Hope it helps you

please please please please mark me braniliest ✔️✔️✔️✔️

Answer 2

THEORAM:-

the line segment joining the mid point of two sides of a triangle is parallel to the third side.

GIVEN:-ABCD is a triangle where E and F are mid point of AB and AC respectively.TO PROVE :-

EF || BC

CONSTRUCTION:-through C draw a line segment parallel to AB &extend EF to meet this line at D.

PROOF:-

SINCE, AB || CD (by construction) with transfers ED.

$\rightarrow$.°. <AEF = <CDF (alternate angle)...(1)

in triangle ΔAEF &ΔCDF.

$\rightarrow$ <AEF = <CDF (from 1)

$\rightarrow$<AEF = <CFD (vertically opposite angles)

$\rightarrow$.°. AF = CF ( as F is mid point of AC).

$\rightarrow$ .°.ΔAEF = ΔCDF ( AAS rule)

$\rightarrow$so, EA = DC (CPCT)

but, EA =EB

hence, EB=DC .

now, in EBCD,

.°. EB || DC

$\rightarrow$ .°.EB=DC

thus, one pair of opposite sides is equal and parallel. hence,

$\rightarrow$EBCD is a parallelogram.

since, opposite sides of parallelogram are parallel. so, ED || BC.

$\rightarrow$ I. e , EF || BC.

[HENCE PROVED. ]