Complete the paragraph proof: It is given that _TUW = SRW and RSTU.
Because ZRWS and UWT are vertical angles and
vertical angles are congruent, CRWS = ZUWT. Then,
by AAS, ATUWA ASRW. Because CPCTC, SW
TW and WU RW. Because of the definition of
congruence, SW = TW and WU = RW. If we add
those equations together, SW + WU = TW + RW.
Because of segment addition, SW + WU = SU and
TW + RW = TR. Then by substitution, SU = TR. If
segments are equal, then they are congruent, so SU
TR. Because of V, ATRS & ASUT, and
because of
ZRST – ZUTS.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

b, i believe, but not sure.