Question

The intercepts made by 3 parallel lines on a transverse line $\left(l_1\right)$ are in the ratio 1 : 1. A second transverse line $\left(l_2\right)$ making angle of ${30}^{\circ }$ with $l_1$ is drawn. The corresponding intercepts on $l_2$ are in the ratio:

• A. $1:1$
• B. $2:1$
• C. $1:2$
• D. $1:3$

Answer 1

The correct option is A $1:1$

The Triangle Proportionality Theorem states that if a line is parallel to one side of a triangle and it intersects the other two sides, then it divides those sides proportionally.

On extending the tranversals $l1$ and $l2$, they join at $A$. join the other two ends with line $BC$ , forming a triangle $-△ABC$

$\therefore \frac{AB}{BC}=\frac{PQ}{QR}$

Given

$\frac{AB}{BC}=\frac{1}{1}$

$\therefore \frac{PQ}{QR}=\frac{1}{1}$ .

This can also be solved as below:

If three parallel lines are intercepted by 2 transversals, in such a way that the two intercepts on one traversal are equal, then the intercepts formed by the other transversal are also equal.

Given

$\frac{AB}{BC}=\frac{1}{1}⟹AB=BC$

$\therefore \frac{PQ}{QR}=\frac{1}{1}$