Question

If $l,m,n$ are three parallel lines and the transversal $t_1$ and $t_2$ cut the lines $l,m,n$ at the points $A,B,C$ and $P,O,R$ as shown in the figure, then

• A. $\frac{AB}{BC}=\frac{PO}{OR}$
• B. $\frac{AB}{OR}=\frac{BC}{PO}$
• C. $\frac{AP}{BO}=\frac{BO}{CR}$
• D. $\frac{AB}{PO}=\frac{AP}{BO}$

Answer 1

The correct option is A $\frac{AB}{BC}=\frac{PO}{OR}$

In triangle ABD and ACE
$\angle A$ is common
$\angle D=\angle E=90$
$\angle ABD=\angle ACE$ (since m || n)

Thus both the triangle are similar.

Hence, $\frac{AB}{BC}=\frac{AD}{DE}$
Similarly, triangle PRT and POS are similar

Hence, $\frac{PO}{OR}=\frac{PS}{ST}$
Since, $l||m||n$, the perpendicular distance between them will be equal.

Hence, $AD=PS$ and $DE=ST$

or, $\frac{AB}{BC}=\frac{PO}{OR}$