For the transformation to be defined as a rotation, which statements must be true? check all that apply.

a) the segment connecting the center of rotation, c, to a point on the pre-image (figure 1) is equal in length to the segment that connects the center of rotation to its corresponding point on the image (figure 2).

b) the transformation is rigid.

c) every point on figure 1 moves through the same angle of rotation about the center of rotation, c, to create figure 2.

d) segment cp is parallel to segment cp'.

e) if figure 1 is rotated 360° about point c, it will be mapped onto itself.

Options 1 and 2). Rotation is a transformation that preserves figure sizes and distances. Such transformations are called rigid. So options 1 and 2 are true.

Option 3). Statement "Every point on figure 1 moves through the same angle of rotation about the center of rotation, C, to create figure 2" is true, it immediately follows from the definition of rotation.

Option 4). If you connect points C and P', you can see that segments CP and CP' are perpendicular, thus not parallel. This option is false.

Option 5). Statement "If figure 1 is rotated 360° about point C, it will be mapped onto itself" is also true, because rotation by 360° has a rule (x,y)→(x,y) - each point's image is the initial point.

correct options are 1, 2, 3 and 5.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

i need a picture

step-by-step explanation: