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Identify congruent figures

Congruent figures have exactly the same shape and size: their corresponding side lengths and angle measures match, even when one figure is translated, rotated, or reflected. Identification focuses on comparing corresponding parts and understanding that position or orientation does not change congruence; scaling, formal proofs, coordinate rules, and the broader relationship between congruence and similarity are not included.

Detailed Explanation: 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 ABCDABCD has side lengths:

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

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

Rectangle EFGHEFGH has side lengths:

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

All four angles are also 90∘90^\circ.

The second rectangle may be turned so that its 66-inch sides match the 66-inch sides of the first rectangle and its 33-inch sides match the 33-inch sides. Every matching angle is also equal.

Therefore, rectangles ABCDABCD and EFGHEFGH are congruent. Turning the second rectangle does not change its shape or size.

Learn by doing: Identify congruent figures

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    2D Shape Congruent or Similar - Image Pair and Property to Yes/No

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