Without solving for "x", which criteria can be used to prove the triangles congruent? Justify.

prove that the side lengths match up with each other. prove that the angles have the same degreee.

make sure the center is the same (could be circumcenter, incenter, orthocenter, etc.)

ASA; right angles CAD and CEB are congruent; AC≅ EC; vertical angles ACD and ECB are congruent;

Step-by-step explanation:

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'.