HELP ASAP! Draw AB and construct its perpendicular bisector. Identify point C on the bisector. Measure the distance from point C to point A and from point C to point B. What theorem does your measurement justify? Explain your answer.

Pythagorean theorem

Step-by-step explanation:

Since perpendicular segment is bisector of AB, the distance from A and B to the intersection is equal

Also the angle between those lines is right angle

The distance from C to AB is the line segment that is common side of the triangles formed by connecting end points

So the distance AC = BC as hypotenuse of congruent right triangles

This measurement justifies Pythagorean theorem

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'.