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The straight lines M1: y - x = 0 and M2: 2x + y = 0 meet at point P. The bisector of the acute angle formed by M1 and M2 cuts the line M3: y + 2 = 0 at point R. Consider the following statements: Statement-1: The ratio PR : RQ is 2\sqrt{2} : 5\sqrt{5}. Statement-2: In every triangle, an angle bisector divides the triangle into two similar triangles.

1. Statement-1 is correct, Statement-2 is correct; Statement-2 does not correctly explain Statement-1.
2. Statement-1 is correct, Statement-2 is incorrect.
3. Statement-1 is incorrect, Statement-2 is correct.
4. Statement-1 is correct, Statement-2 is correct; Statement-2 correctly explains Statement-1.

Correct answer: Statement-1 is correct, Statement-2 is incorrect.

Solution

Statement-1 is correct as it accurately describes the ratio of segments created by the angle bisector, while Statement-2 is incorrect because it misrepresents the relationship between the angle bisector and the triangles formed; the angle bisector does not necessarily create similar triangles in all cases.

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