Question

$X$ and $Y$ are points on the sides $PQ$ and $PR$ respectively, of a $\triangle PQR$ . If the lengths of $PX$ , $QX$ , $PY$ and $YR$ (in cm) are 4, 4.5, 8 and 9 respectively, then show that $XY \parallel QR$ .

Accepted Answer

Calculate the ratios of segments on sides $PQ$ and $PR$: $$\frac{PX}{QX} = \frac{4}{4.5} = \frac{8}{9}$$ $$\frac{PY}{YR} = \frac{8}{9}$$ Since $\frac{PX}{QX} = \frac{PY}{YR}$, by the converse of Basic Proportionality Theorem (BPT), $XY \parallel QR$.

Converse of Thales Theorem in a triangle

Explanation

Practise this under board exam conditions