L1:y−x=0 L2:2x+y=0 L3:y+2=0 On solving the equation of line L1 and L2 we get their point of intersection (0,0) i.e., origin O. On solving the equation of line L1 and L3, we get P=(−2,−2). Similarly, solving equation of line L2 and L3, we get Q=(−1,−2) We know that bisector of an angle of a triangle, divide the opposite side the triangle in the ratio of the sides including the angle [Angle Bisector Theorem of a Triangle] ∴
PR
RQ
=
OP
OQ
=
√(−2)2+(−2)2
√(−1)2+(−2)2
=
2√2
√5
∴ Statement 1 is true but ∠OPR≠∠OQR So ∆OPR and ∆OQR not similar ∴ Statement 2 is false