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Every Point on the Bisector of an Angle Is Equidistant from the Sides of the Angle.

In the figure...

Question

In the figure, Ray $Y M$ is the bisector of $∠ X Y Z$ , where $X Y = Y Z$ . Find the relation between $X M$ and $M Z$ .
Answer: $s e g X M ≅ s e g M Z$
If true then enter 1 else if False enter 0

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Solution

Given : $Y M$ bisects $∠ X Y Z$ , $X Y = Y Z$
In $△ X Y Z$ ,
$\frac{X Y}{Y Z} = \frac{X M}{M Z}$ (Angle bisector theorem)
$1 = \frac{X M}{M Z}$ ( $X Y = Y Z$ )
$X M = M Z$

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