Question

Explain Basic proportionality theorem.

Answer 1

Just think what happens if a line intersects two sides of a triangle. It will actually two sides in two different parts each, isn't it ? Any line will do that.
But what if, that line is parallel to the third line ? See figure below

PQ is the line which intersects AB and AC and PQ is parallel to BC.
Can you see something uniqu about the lines AB and AC ? There seems to be some similarity between the length of AP compared to AB & AQ compared to AC ??
Basic proporationality theorem states, that when a line parallel to third side intersects other two lines, then it cuts other two lines proportionately.
In other ratio $\frac{AP}{PB}$ will be equal to ratio $\frac{AQ}{QC}.$