Prove that the external angle bisectors of a triangle intersect their opposite sides at three collinear points.

In triangle $△PQR$, $E$ and $F$ are points on the sides $PQ$ and $PR$ respectively. Given $\mathrm{PQ}=1.28 \mathrm{cm}, \mathrm{PR}=2.56 \mathrm{cm}, \mathrm{PE}=1.8 \mathrm{cm}$ and $\mathrm{PF}=3.6 \mathrm{cm}$. State whether $EF\parallel QR$ or not?

Using the converse of Basic Proportionality Theorem (BPT), prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side.

If figure $\mathrm{OPRQ}$ is a square and $\angle \mathrm{MLN}=90°.$ Prove that $△\mathrm{QMO}~△\mathrm{RPN}$.

In the given figure, state if $PQ\parallel EF$.

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