Question

In triangle PQR seg PM is a median. Angle bisectors of angle PMQ and angle PMR intersect side PQ and side PR in points X and Y respectively. Prove that XY is parallel to QR.

Answer 1

Answer:

To Prove : X Y ║QR

Proof:

  PM is median .

QM=MR-----(1)

M X is angle bisector of ∠PMQ.

As, well as, M Y is angle bisector of ∠PMR.

Angle bisector theorem states that, the Ratio of two adjacent sides of the angle which is bisected, is equal to ratio of the segments where the bisector meets the third side.

$2.\frac{MP}{MQ}=\frac{PX}{XQ}\\\\ 3. \frac{PM}{MR}=\frac{PY}{YR}$

Equating ,(1), (2) and (3), we get

$\frac{PX}{XQ}=\frac{PY}{YR}$

As, Basic proportionality theorem states that , if a line or line segment divides the two sides in equivalent ratio,then that line is parallel to third side.

So, XY ║QR