Congruency: Congruent Triangles
122. Coincide & Congruent · Same shape, same size, perfect match
Triangle DEF is always congruent to Triangle ABC.
Two triangles are congruent (≅) if they have the same shape AND the same size. One can be slid, rotated, or flipped to land exactly onto the other. We write ΔABC ≅ ΔDEF when A↔D, B↔E, C↔F.
What this lesson covers
Try to break it
Drag M to slide and R to rotate triangle DEF. With these moves you can land it exactly on ABC. Now imagine you could also stretch DEF — that would break the match. Congruence allows sliding, rotating, and flipping, but never resizing.
The proof, step by step
Prove that triangle DEF is congruent to triangle ABC.
- Two figures are congruent if they have the same shape and size.
- When placed over each other, corresponding parts coincide exactly.
- Congruence is denoted by the symbol ≅.
Worked example
Two triangles are said to be congruent if, on placing one over the other, they coincide exactly. This means they have the same:
Congruent figures must be identical in both shape and size. When one is placed over the other, all corresponding sides and angles coincide exactly.
- Same shape only
- Same size only
- Same shape and size — correct
- Same perimeter only