5. Next time include the entire page in the photo. I'm guessing it's U at the top right and O at the bottom right.
First box.
SE ≅ SU
Given
Second box
angle 1 ≅ angle 2
Those are vertical angles, which are always congruent
Third box
angle E = angle U
Given
Next box, three arrows in.
triangle MES ≅ triangle OUS
Angle - Side - Angle
Last box:
MS ≅ SO
Corresponding parts of congruent triangles.
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6.
First box:
angle E ≅ angle U
Given
Second box:
NS ≅ NS
reflexivity (aka it's the same segment)
Third box:
angle 1 = angle 2
Definition of angle bisector
Next box:
triangle WNS ≅ triangle ENS
Angle - Side - Angle
Next:
WN ≅ EN
Corresponding parts of congruent triangles.