Recognize congruent figures

Detailed Explanation: Recognize congruent figures

Two figures are congruent when they have the same shape and the same size. One figure may be moved by a slide, turn, or flip, but it cannot be stretched or shrunk.

To check, compare:

1. The number of sides and their arrangement.
2. Corresponding side lengths.
3. Corresponding angle measures.
4. Whether one figure could be moved onto the other using only slides, turns, or flips.

Example

Are rectangle $ABCD$ and rectangle $EFGH$ congruent?

Rectangle $ABCD$ has side lengths $5$ units and $3$ units. Rectangle $EFGH$ also has side lengths $5$ units and $3$ units. All four angles in both rectangles are right angles.

Step 1: Compare the shapes.
Both figures are rectangles, so they have the same arrangement of sides and angles.

Step 2: Compare the side lengths.
The corresponding side lengths match:

• Long sides: $5=5$
• Short sides: $3=3$

Step 3: Compare the angles.
Every angle is a right angle, so all corresponding angles measure $90^\circ$.

Step 4: Think about a rigid motion.
One rectangle may be turned so that its $5$-unit sides and $3$-unit sides point in the same directions as the other rectangle. Then it can be slid into place. Turning and sliding do not change its size or shape.

Therefore, the rectangles are congruent:

If one rectangle had side lengths $10$ units and $6$ units, it would have the same shape but a different size. Those figures would be similar, not congruent.