# PQRS is a parallelogram and line segment PX, RY bisect angle P and R respectively.Show that PX and RY are parallel.

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To prove: PX║RY

Proof:∠P =∠R

1/2∠P=1/2∠R_______(1)

in ΔPSX and RQY

PS =QR(sides of a ║gm)

∠S = ∠Q(opposite sides)

∠SPX = ∠YRQ (FROM 1)

∴ΔPSX=ΔRQY

from CPCT we get

SX = QY

⇒PY = XR (PQ-QY=SR-SX)

PY║XR (as PQ ║SR)

∴PYRX is a parallelogram

⇒PX║RY (opposite sides of a ║gm)