First Criterion for Similarity of Triangles (AA Similarity)
📐 What is Similarity of Triangles?
Two triangles are said to be similar if they have the same shape but not necessarily the same size. Think of it like a photograph and its enlarged version — same shape, different size!
When two triangles are similar:
- ✅ Their corresponding angles are equal
- ✅ Their corresponding sides are in the same ratio (proportional)
We write: $\triangle ABC \sim \triangle DEF$ (read as "triangle ABC is similar to triangle DEF")
⭐ The AA (Angle-Angle) Similarity Criterion
THEOREM (AA Similarity)
If in two triangles, two pairs of corresponding angles are equal, then the two triangles are similar.
In formal notation:
If in $\triangle ABC$ and $\triangle DEF$:
$\angle A = \angle D$ and $\angle B = \angle E$
Then $\triangle ABC \sim \triangle DEF$
🤔 Why only TWO angles?
Remember: The sum of all angles in a triangle is always $180°$. So if two angles of one triangle equal two angles of another triangle, the third angle must automatically be equal too!
$\angle C = 180° - \angle A - \angle B = 180° - \angle D - \angle E = \angle F$
This is why we only need to check two pairs of angles — the third pair takes care of itself!