Can You Get There From Here?

Learning Focus

Connect rigid motions to congruence: congruent figures are related by a sequence of rigid motions.

Big idea

Two figures are congruent if and only if a sequence of rigid motions maps one onto the other.

• Corresponding sides are equal; corresponding angles are equal.
• Dilations change size, so they do not show congruence.
• Perimeter and area are preserved by rigid motions.

Worked example

Triangle $A(0,0),B(3,0),C(0,4)$ is translated by $(x+5,y+2)$.

The image is congruent to the original, so its sides are $3,4,5$ and its perimeter is $3+4+5=12$.

A triangle with sides $6,8,10$ is not congruent to it; it is a dilation by $2$.

Takeaways

• Congruent means a rigid-motion sequence exists.
• Corresponding parts match.
• Different size means not congruent.