Skill: Identify congruent figures

Two figures are congruent when they have exactly the same shape and size. They may be moved, turned, or flipped, but their matching sides and angles must stay the same.

To check:

1. Match each side of one figure with the corresponding side of the other.
2. Compare the side lengths.
3. Compare the angle measures.
4. Ignore the figures’ positions or directions.

Example:
Rectangle $ABCD$ has side lengths:

• $AB=6$ inches
• $BC=3$ inches
• $CD=6$ inches
• $DA=3$ inches

All four angles are right angles, or $90^\circ$.

Rectangle $EFGH$ has side lengths:

• $EF=3$ inches
• $FG=6$ inches
• $GH=3$ inches
• $HE=6$ inches

All four angles are also $90^\circ$.

The second rectangle may be turned so that its $6$-inch sides match the $6$-inch sides of the first rectangle and its $3$-inch sides match the $3$-inch sides. Every matching angle is also equal.

Therefore, rectangles $ABCD$ and $EFGH$ are congruent. Turning the second rectangle does not change its shape or size.