First one
1. XW≅ZW 1. Given It's good to start with given
2.∠XWY ≅ ∠ZWY 2. Given Again, get the given out of the way
3.WY ≅ WY 3. Reflexive This reason basically means that the line is equal to itself
4.ΔXWY ≅ZWY 4. SAS We have a side, an angle and a side: SAS
Second Problem
Again, let's get the givens out of the way. I'm lazy, so just put the things in the given section in the boxes.
3. Vertical angles This is just a fun way of saying that the angles on top of each other are equal
4. AAS We have an angle, an angle and a side. Whack em' together and you get AAS
this should be ok by now lmk if its not.