Question

Study the adjoining figure. Write the ratios in relation to basic proportionality theorem, in terms of $a,b,c$ and $d$.

Answer 1

Consider two triangles $PXY$ and $PQR$

$PQ=PX+XQ=a+b$

$PR=PY+YR=c+d$

$\therefore \frac{PX}{PQ}=\frac{a}{a+b}$

$\frac{PY}{PR}=\frac{c}{c+d}$

$\therefore \frac{PX}{XQ}=\frac{a}{b};\frac{PY}{YR}=\frac{c}{d}$

By Basic Proportionality Theorem, if a line is parallel to a triangle which intersects the other sides into two distinct points, then the line divides the sides in proportion.

Here, $XY||QR$