In Delta XYZ,the bisector of angle X intersec | vedclass

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(A) According to the Angle Bisector Theorem,if a ray bisects an angle of a triangle,it divides the opposite side into segments that are proportional t

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$2.4$

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(A) According to the Angle Bisector Theorem,if a ray bisects an angle of a triangle,it divides the opposite side into segments that are proportional to the other two sides of the triangle.In $\Delta XYZ$,$XM$ is the bisector of $\angle X$,so:$\frac{XY}{XZ} = \frac{YM}{MZ}$Given $XY = 3.6$,$XZ = 4.2$,and $MZ = 2.8$.Substituting the values:$\frac{3.6}{4.2} = \frac{YM}{2.8}$$YM = \frac{3.6 	imes 2.8}{4.2}$$YM = \frac{3.6 	imes 2}{3} = 1.2 	imes 2 = 2.4$Therefore,$YM = 2.4$.

In $\Delta XYZ$,the bisector of $\angle X$ intersects $\overline{YZ}$ at $M$. If $XY = 3.6$,$XZ = 4.2$ and $MZ = 2.8$,find $YM$.

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