Question

explain the converse of thale's theorem​

Answer 1

Answer:

hii mate✌️,

Step-by-step explanation:

The converse of thale's theorem states that

${ \red{if \: a \: line \: divides \: any \: two \: sides \: of \: a \: triangle \: in \: the \: same \: ratio \: then \: the \: line \: is \: parallel \: to \: third \: side}}$

we are given that the sides are in same ratio

$\frac{ad}{db} = \frac{ae}{ec}$

${ \orange{if \: de \: is \: not \: parallel \: to \: bc \: \: draw \: a \: line \: de1 \: parallel \: to \: bc}}$

${ \huge{so}} \: \: \frac{ad}{db} = \frac{ae1}{e1c}$

$therefore \: \frac{ae}{ec} = \frac{ae1}{e1c}$

$but \: if \: they \: are \: equal \: then \: they \: should \: coincide \: which \: they \: are \: not$

${ \huge{hence}} \: { \green{de \: is \: parallel \: to \: bc}}$

$\huge{ \orange \ \fcolorbox{aqua}{aqua}{follow \: me}}$

Answer 2

Answer:

If a line divides any two sides of a triangle in the same ratio, then the line must be parallel to the third side.