
Is ΔRST ΔMNO?
By the definition of congruent, we need to find a rigid motion that will map ΔRST onto ΔMNO.
Rigid motion: Reflection
A reflection over line l will map ΔRST to coincide with ΔMNO, making
ΔRST ΔMNO. 

Is ΔABC ΔDEF?
By the definition of congruent, we need to find a rigid motion that will map ΔABC onto ΔDEF.
Rigid motion: Reflection
A reflection over the yaxis will map ΔABC to coincide with ΔDEF, making
ΔABC ΔDEF. 

We need to find a rigid motion that will map one parallelogram onto the other.
Rigid motion: Translation
The translation (x, y) → (x + 4, y  4) will map PQRS onto TUVW, making
PQRS TUVW. 

Is ΔEFG ΔJKL?
We need to find a rigid motion that will map one triangle onto the other.
Rigid motion: Rotation
A rotation of 90º about the origin will map ΔEFG to coincide with ΔJKL, making
ΔEFG ΔJKL. 

Is ΔBCD ΔEFG?
Sometimes a combination of rigid motions is needed to map one figure onto another.
Rigid motions: Reflection and Translation
Assuming and are horizontal, reflect ΔBDC over a horizontal line halfway between and. Then translate the image horizontally to the right to coincide with ΔEFG making ΔBCD ΔEFG. 

Is ΔABC ΔDEF?
We need to find a combination of rigid motions that will map one triangle onto the other.
Rigid motions: Reflection and Translation
A reflection in the xaxis, followed by a translation of (x, y) → (x  6, y + 1), will map ΔABC to coincide with ΔDEF, making
ΔABC ΔDEF. 