Question

If there are three or more parallel line and the intercepts made by them on one transversal are equal prove that the corresponding intercepts on any other transversal are also equal.

Answer 1

Let $l,m,n$ are three paralle lines intersected by transversals $p$ and $q$ suvh that $l,m$ and $n$ cutt off equal intercept $AB$ and $BC$ on $p$.

we have to prove $l,m$ and $n$ cut off equal intercept $DE$ and $EF$ on $q$ also.

Proof : Join $AF$, Suppose it intersects line $m$ at $G$

In $△ACF,B$ is midpoint of $AC$ because $(AB=BC)$

and $BG$ is parallel to $CF$

$\therefore$ $G$ is mid point of $AF$ by converse of midpoint theorem

In $△AFD,G$ is mid point of $AF$ and $GE\parallel AD$

$\because E$ is midpoint of $DF$

$\Rightarrow DE=EF$

Hence $l,m$ and $n$ cut off equal intercepts $DE$ and $EF$ on $q$.