If a part of the image matches up with a part of the original figure, we call them corresponding parts. The part could be an angle, point, or side. We can find corresponding angles, corresponding points, or corresponding sides.

If two figures are congruent, then there is a rigid transformation that takes one figure onto the other. The same rigid transformation can also be applied to individual parts of the figure, such as segments and angles, because rigid transformations act on every point on the plane. Therefore, the corresponding parts of two congruent figures are congruent to each other.

Using a translation and a rotation we can take quadrilateral to quadrilateral . Now that we know the two figures are congruent, we also know that all the corresponding parts are congruent. Each of these statements (and more!) must be true:

• Angle is congruent to angle .
• Segment is congruent to segment .
• Angle is congruent to angle .
• Segment is congruent to segment .