First Triangle Congruence Criterion
Side-Angle-Side (SAS)
One of the most powerful tools in geometry — proving two triangles are identical using just three pieces of information!
📐 What Are Congruent Figures?
Definition:
Two figures are congruent if they have the same shape and the same size. One figure can be placed exactly on top of the other so that every point matches perfectly.
Think of congruent figures like identical puzzle pieces — if you pick one up and place it on the other, they overlap perfectly. You might need to flip or rotate one piece, but they will always fit exactly.
- ✓ Same shape
- ✓ Same size
- ✓ All corresponding parts are equal
- ✓ One can be placed exactly on top of the other
🔺 Congruent Triangles — Formal Definition
Definition of Congruent Triangles
Two triangles are congruent if all corresponding sides are equal AND all corresponding angles are equal.
That means six equalities in total: 3 pairs of sides + 3 pairs of angles.
Notation for Congruence
The symbol ≅ means "is congruent to."
We write: △ABC ≅ △DEF
△ABC ≅ △DEF tells us exactly which vertices correspond:
- A corresponds to D
- B corresponds to E
- C corresponds to F
Corresponding Parts
If △ABC ≅ △DEF, then:
| Sides | Angles |
|---|---|
| AB = DE | ∠A = ∠D |
| BC = EF | ∠B = ∠E |
| AC = DF | ∠C = ∠F |
That's 6 equalities total!