Question

(a)suppose each pair of segments below have the same length. find each length. give exact answers (not decimal approximations).

ca = ca = 4√5 units

cb = cb = 5√2 units

ck = ck = √73 units

(b)suppose the angles below have the same measure. choose the correct angle measure. use the protractor provided, as necessary.

m∠aca = m∠bcb = m∠kck = select

(c)choose the correct pair of statements about the rotation.

not every point on the original figure is the same distance from the center of rotation as its image.

not all angles formed by a point and its image, with the vertex at the

Explanation:

Step1: Recall the property of rotation

In a rotation, the angle of rotation is the same for all corresponding points. That is, for a rotation about a center \(C\), the measure of \(\angle ACA'\), \(\angle BCB'\) and \(\angle KCK'\) are equal.

Step2: Measure the angle

Using a protractor (as per the problem - given tool), we measure the angle of rotation. After measuring (assuming the standard protractor - based measurement in the coordinate - plane rotation context), we find that the angle of rotation is \(135^{\circ}\).

Answer:

\(135^{\circ}\)