Congruent Figures
Learning about figures that are identical in shape and size.
Core concept
Congruence is different from similarity — congruent figures must be identical in both shape and size, while similar figures only need the same shape (proportional sizes are allowed). Testing for congruence is fundamental in geometric proofs, and real-world applications include manufacturing (ensuring identical parts, like bolts of the same size, are truly congruent) and quality control processes.
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• Congruent figures have exactly the same shape and size.
• Congruent triangles have equal corresponding sides and equal corresponding angles.
• Tests for triangle congruence include SSS and SAS.
• Congruence differs from similarity, which only requires the same shape, not necessarily the same size.