Question

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

Answer 1

PQRS is a parallelogram and PX bisects ∠P and RY bisects ∠R

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)