Angle Bisector Theorem
The Angle Bisector Theorem states that in a triangle, if a line segment divides an angle into two equal angles, then it divides the opposite side into two segments that are proportional to the lengths of the other two sides
The Angle Bisector Theorem states that in a triangle, if a line segment divides an angle into two equal angles, then it divides the opposite side into two segments that are proportional to the lengths of the other two sides.
More formally, let’s consider a triangle ABC and a line segment DE that bisects angle BAC. The theorem states that the following ratio is true:
|BD| / |DC| = |AB| / |AC|
Here, |BD| represents the length of segment BD, |DC| represents the length of segment DC, |AB| represents the length of side AB, and |AC| represents the length of side AC.
In other words, the ratio of the lengths of the segments formed by the angle bisector on the opposite side of the triangle is equal to the ratio of the lengths of the other two sides of the triangle.
This theorem is useful in various geometric problems and proofs. It helps establish relationships between the lengths of segments in a triangle when an angle bisector is involved.
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