Question

X is a point in the interior of $△$ DEF joined to its vertices D, E and F. From a point P on DX, PQ is drawn parallel to DE, meeting XE at Q. QR is drawn parallel to EF meeting XF at R. Which of the following is correct?

• A. PQ $\parallel$ DF
• B. QR $\parallel$ DF
• C. PR $\parallel$ DF
• D. PQ $\parallel$ QR

Answer 1

The correct option is C PR $\parallel$ DF

As can be seen from the figure, using the information given in the passage

If $PQ||ED$, => implies that $\frac{XP}{PD}=\frac{XQ}{EQ}$

If $QR||EF$,=> implies that $\frac{XQ}{QE}=\frac{XR}{RF}$

Using both the equations, we can say that $\frac{XP}{PD}=\frac{XR}{RF}$

This implies that $PR||DF$