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Question
In the figure, ray YM is the bisector of ∠XYZ, where seg XY ≅ seg YZ, find the relation between XM and MZ.
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Solution 1
Given : YM bisects ∠XYZ, XY = YZ
In ΔXYZ,
`(XY)/(YZ)=(XM)/(MZ)` (Angle bisector theorem)
1 = `(XM)/(MZ) ` (XY = YZ)
XM = MZ
Solution 2
Given : YM bisects ∠XYZ, XY = YZ
In ΔXYZ,
`(XY)/(YZ)=(XM)/(MZ)` (Angle bisector theorem)
1 = `(XM)/(MZ) ` (XY = YZ)
XM = MZ
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