Remember that an isometry is a rigid motion. That is, it preserves angle measures and side lengths.
Congruent.
Practice makes perfect
Let's begin by remembering the definition of congruent figures.
Congruent Figures
Two figures are congruent if and only if there is a sequence of one or more rigid motions that maps one figure onto the other.
Remember that rigid motions are called isometries. There is one more important fact.
The composition of two or more isometries
is an isometry.
Finally, notice that a sequence of one or more rigid motions is a composition of isometries, which is an isometry. Then, we can rewrite the definition of congruent figures as follows.
Congruent Figures
Two figures are congruent if and only if there is an isometry that maps one figure onto the other.
Therefore, the missing word in the given definition is congruent.
Congruent Figures
If two figures are congruent, then there is an isometry that maps one figure onto the other.
Alternative Solution
Alternative Solution
Recall that an isometry preserves angle measures and side lengths. So, if it maps one figure onto another, then the figures must be congruent. Consequently, the missing word is congruent.
Congruent Figures
If two figures are congruent, then there is an isometry that maps one figure onto the other.
