Angle Bisector Theorem

An angle bisector cut an angle precisely in half. One important property of edge bisectors is the if a allude is top top the bisector of one angle, then the point is equidistant from the political parties of the angle. This is dubbed the Angle Bisector Theorem.

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In various other words, if (overrightarrowBD) bisects (angle ABC), (overrightarrowBAperp FDoverlineAB), and, (overrightarrowBCperp overlineDG) climate (FD=DG).

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Figure (PageIndex1)

The converse the this organize is also true.

Angle Bisector theorem Converse: If a suggest is in the inner of one angle and also equidistant from the sides, climate it lies on the bisector of the angle.

When we construct angle bisectors because that the angles of a triangle, they satisfy in one point. This point is dubbed the incenter the the triangle.

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Solution

No since (B) is not necessarily equidistant from (overlineAC) and (overlineAD). We do not recognize if the angles in the diagram are appropriate angles.


Example (PageIndex2)

A (108^circ) edge is bisected. What are the steps of the result angles?

Solution

We recognize that come bisect means to cut in half, so each of the resulting angles will be half of 108. The measure up of each resulting angle is (54^circ).


Example (PageIndex3)

Is (Y) top top the angle bisector the (angle XWZ)?

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Example (PageIndex5)

(overrightarrowAB) is the edge bisector that (angle CAD). Fix for the lacking variable.

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