Straight Lines And Pair Of Straight Lines

Lines \(\mathrm{L}_{1}: y-x=0\) and \(\mathrm{L}_{2}: 2 x+y=0\) intersect the line \(\mathrm{L}_{3}: y+2=0\) at \(\mathrm{P}\) and \(\mathrm{Q}\), respectively. The bisector of the acute angle between \(L_{1}\) and \(L_{2}\) intersects \(L_{3}\) at \(R\).

STATEMENT - 1 : The ratio PR : RQ equals \(2 \sqrt{2}: \sqrt{5}\).

STATEMENT - 2 : In any triangle, bisector of an angle divides the triangle into two similar triangles.