Triangle XYZ is equilateral, Line segment WY bisects angle XYZ. Prove that Line segment XW is congruent to Line segment ZW

Question

I need the answer to this proof. 

Answer 1

First I would suggest drawing it so its easier to see whats happening. 

 

For the process:

First: with an equilateral triangle all the side and all the angles are equal.

Second:after bisecting <xyz, angles <wyx and <wyz must be equal, definition of a bisector

 

statements:

<yxw=<yzw   -equilateral triangle

yx=yz            -equilateral triangle

<wyz=<wyz   -bisector

Using ASA postulate (angle, side, angle) the triangles wyx and wyz are congruent, therefore all parts must be congruent.

wx and wz must be congruent

 

You can also use SAS with 

wy=wy             -anything equals itself

<wyz=<wyz     -bisector

yx=yz             -equilateral triangle

 

You'll notice both need to use the bisector to prove that the angles of the two created triangles are equal, which is then combined with information about how the equilateral triangles are equivalent, or how something is equivalent to itself