The question is: divide a line segment 6 cm long in the ratio of 4:3. Prove your assertion . I drew this diagram but how will i prove it ? PLS TELL ME HOW TO PROVE THIS ?? ! DONT TELL ME TO CORRECT MY CONSTRUCTION AS ITS ALREADY CORRECT 

Dear Student,

You can prove your assertion in following ways.

Method 1:- from the diagram it is evident that line A-A4 is parallel to line B-B3
​therefore $$\begin{gathered} \angle A=\angle B (corresponding angles) \\ \angle BCB3=\angle ACA4 (Vertical opposite angles) \\ hence by AA, △ACA4 and △BCB3 are similiar \\ in similiar traingles the sides are proportionate \\ \Rightarrow \frac{A-A4}{B-B3}=\frac{AC}{BC} \\ as length of A-A4=4 cm \\ length of B-B4=3 cm \\ thus \frac{AC}{BC}=\frac{4}{3} \end{gathered}$$
Method 2-

as the line AB is to be divided into ratio $\frac{4}{3}$
hence length of AC= $$\begin{gathered} \frac{4}{7}\times 6=\frac{24}{7} \\ =3.4 \end{gathered}$$
length of BC= 
$$\begin{gathered} \frac{3}{7}\times 6=\frac{18}{7} \\ =2.6 \end{gathered}$$

If we measure the length of AC and BC it should match with above values.

Regards,