Question

This construction can be used to prove the angle bisector theorem. What is the angle bisector theorem?

1) A theorem that states that the angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.
2) A theorem that states that the angle bisector of a triangle divides the opposite side into two segments that are equal in length.
3) A theorem that states that the angle bisector of a triangle divides the opposite side into two segments that are perpendicular to each other.
4) A theorem that states that the angle bisector of a triangle divides the opposite side into two segments that are parallel to each other.

Answer 1

The Angle Bisector Theorem states that the angle bisector of a triangle divides the opposite side into two segments proportional to the remaining two sides. This theorem is fundamental to understanding triangle properties in geometry.

Step-by-step explanation:

The Angle Bisector Theorem is a fundamental result in geometry that is particularly relevant to triangle properties. This theorem states that for any triangle, the bisector of an angle divides the opposite side into two segments that are proportional to the other two sides of the triangle. Specifically, the theorem is articulated as: if a bisector of an angle of a triangle divides the opposite side into two segments, those two segments are in the same ratio as the other two sides of the triangle.

Therefore, the correct answer is: 1) A theorem that states that the angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle. This theorem is distinct from the Pythagorean Theorem, which deals with the sides of a right-angled triangle, or trigonometric functions, which involve the ratios of the sides of a right-angled triangle to its angles.