How Do You Spell ANGLE BISECTOR THEOREM?

Pronunciation: [ˈaŋɡə͡l ba͡ɪsˈɛktə θˈi͡əɹəm] (IPA)

The angle bisector theorem states that a line bisecting an angle of a triangle divides the opposite side into segments that are proportional to the lengths of the adjacent sides. The spelling of "angle bisector theorem" is represented using the International Phonetic Alphabet (IPA) as "ˈæŋɡəl baɪˈsɛktər ˈθiːərəm". This includes the pronunciation of each individual letter and sound in the word, making it easier for non-native speakers to understand and accurately pronounce the term.

Meaning and Definition
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ANGLE BISECTOR THEOREM Meaning and Definition

  1. The angle bisector theorem is a geometric relationship between the sides of a triangle that are divided by an angle bisector. In a triangle, an angle bisector is a line segment that divides an angle into two congruent angles. The angle bisector theorem states that the ratio of the lengths of two adjacent sides of a triangle is equal to the ratio of the lengths of the segments into which the opposite side is divided by the angle bisector.

    More precisely, let's consider a triangle ABC where angle A is bisected by a line segment AD, with D lying on side BC. According to the angle bisector theorem, the ratio of the length of segment BD to the length of segment CD is equal to the ratio of the length of side AB to the length of side AC. Mathematically, this can be expressed as:

    BD/CD = AB/AC

    This theorem is applicable not only to any specific triangle, but also to any triangle with an angle bisected by a line segment. It establishes a proportionality relationship between the various sides of a triangle and provides a mathematical tool for finding unknown side lengths when the lengths of other sides and/or the angle bisector are known. The angle bisector theorem has various applications in geometry, trigonometry, and other fields of mathematics.