The lines $L_{1}: y-x=0$ and $L_{2}: 2x+y=0$ intersect the line $L_{3}: y+2=0$ at $P$ and $Q$ respectively. The bisector of the acute angle between $L_{1}$ and $L_{2}$ intersects $L_{3}$ at $R$. This question has Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. 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. (1) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1. (2) Statement-1 is true, Statement-2 is false. (3) Statement-1 is false, Statement-2 is true. (4) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
The lines $L_{1}: y-x=0$ and $L_{2}: 2x+y=0$ intersect the line $L_{3}: y+2=0$ at $P$ and $Q$ respectively. The bisector of the acute angle between $L_{1}$ and $L_{2}$ intersects $L_{3}$ at $R$.\\
This question has Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.\\
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.\\
(1) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.\\
(2) Statement-1 is true, Statement-2 is false.\\
(3) Statement-1 is false, Statement-2 is true.\\
(4) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.