Question

state and prove the converse of mid point therom​

Answer 1

Answer:

converse of mid-point theorem: it states that in a triangle line drawn from the mid-point of the one side of triangle, parallel to the other side intersect the third side at its mid-point.

Answer 2

$\large\bf{\underline\orange{Answer \:↝}}$

Que :- State and prove the Converse of Mid Point Therom.

Ans :- Converse of Mid Point Therom

Converse of mid-point theorem: It states that in a triangle line drawn from the mid-point of the one side of triangle, parallel to the other side intersect the third side at its mid-point.

given: ABC is a triangle. and D is the mid-point of AB.

from D a line DE is drawn parallel to BC, intersect AC at E.

TPT: E is the mid-point of AC.

construction: extend DE. from C draw a line CF parallel to BA, which intersect produced DE at F.

proof: since BD is parallel to CF (by the construction)

and DF is parallel to BC (given)

BDFC is a parallelogram.

BD= CF [opposite sides of the parallelogram are equal]

AD= BD [D is the mid-point of AB]

AD= CF......(1)

in the triangle AED and CEF,

∠AED=∠CEF

∠ADE=∠EFC

AD=CF [from (1)]

therefore by the AAS congruency triangles are congruent.

thus AE = EC

i.e. E is the mid-point of AC.