Two-Column Proofs

[XmyXloveXundefined]

I don't understand Two-Column Proofs AT ALL, in the slightest. We've been learning about them for quite some time, and they just cause me a huge headache. I have a limited time to do "make-up work" for my Geometry 1-2 class, but I still don't get it. Help me, please? Here is one of my homework problems.

• |Statments|Reasons|
  1)|XY is congruent to ZW|1)Given
  2)|XZ is congruent to XZ|2)Reflexive Property
  3)|Triangle WXZ is congruent to triangle ZYX| 3)____________
  4)|Angle Y is congruent to Angle W|4)____________

I understand that number 2 is proven by the "Reflexive Property," but I don't know how to prove the rest. :?:

 

[masters]

I don't understand Two-Column Proofs AT ALL, in the slightest. We've been learning about them for quite some time, and they just cause me a huge headache. I have a limited time to do "make-up work" for my Geometry 1-2 class, but I still don't get it. Help me, please? Here is one of my homework problems.

• |Statments|Reasons|
  1)|XY is congruent to ZW|1)Given
  2)|XZ is congruent to XZ|2)Reflexive Property
  3)|Triangle WXZ is congruent to triangle ZYX| 3)____________
  4)|Angle Y is congruent to Angle W|4)____________

I understand that number 2 is proven by the "Reflexive Property," but I don't know how to prove the rest. :?:

Hi XmyXloveXundefined,

You don't seem to have enough information to prove 2 triangles congruent.

First of all there is no diagram. I could assume you have a quadralateral WXYZ with diagonal XZ and one pair of opposite sides congruent.

That would take care of the given: \(\displaystyle \overline{XY} \cong \overline {ZW}\)

and the reflexive property \(\displaystyle \overline{XZ} \cong \overline {XZ}\) in step 2.

But this only gives you 2 sides of each triangle formed by the diagonal to determine if the triangles are congruent.

Not enough info. You need the other side or an the included angle.

And the symbols are off. If \(\displaystyle \triangle WXZ \cong \triangle ZYX\), then XY would have to be congruent to ZX. And that's not what you said in your first statement. So something is amiss.

Describe the diagram for us if this is not right. Did you leave something out??