Two figures that are congruent have which property?

• A. All corresponding sides and all corresponding angles are equal
• B. Only equal perimeters
• C. Only equal areas
• D. Only similar shapes

Answer: (A)

Congruent figures have the same size and shape, so their corresponding parts line up exactly. When two figures are congruent, every side of one has the same length as the matching side of the other, and every angle has the same measure as the matching angle. Because those parts match, the two figures share the same perimeter and the same area as well.

Note that equal perimeters alone can occur for different shapes, and equal areas can occur for shapes that aren’t congruent. Similar shapes have the same angles and proportional sides but can differ in size, which isn’t enough for congruence.