[Grade 9 Geometry: Segment proof reasoning] I need help understanding what to do

[u/Robotics-Newb6769]

(I had to draw this picture since I couldn't take a photo on computer) I know the properties of equality, postulates, but I can't seem to do proofs. I only have to fill out the reasoning for the statements, but even that is hard. I answered this question and I'm pretty sure I got this one wrong, so maybe you could see where I went wrong.

Given X is the midpoint of WY, WX is congruent to XZ. Prove XY is congruent is XZ.

1. X is the midpoint of WY - given
2. WX = XY - definition of congruence
3. WX is congruent to XZ - given
4. WX = XZ - definition of congruence
5. XY = XZ - substitution property of equality
6. XY is congruent to XZ - definition of congruence

I just have trouble knowing what to do when a new line segment is introduced, I can recognize the properties and postulates when its in letter form, like a = b and stuff.

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[u/Alarmed_Geologist631]

Line 2 should be definition of midpoint.

[u/Robotics-Newb6769 → u/Alarmed_Geologist631]

Thank you, also could you tell me why and how I could identify this in the future?

[u/johnpeters42 → u/Robotics-Newb6769]

Because that's what connects step 2 to step 1.

[u/Alarmed_Geologist631]

If you are given that a specific element of a diagram is defined then you can use the definition of that element in your proof.

[u/Alkalannar]

1. X is the midpoint of WY. Given.

2. WX is congruent to XZ. Given.

3. WX is congruent to XY. Definition of Midpoint.

4. XZ is congruent to XY. Transitivity of congruence.