Concept 6.3
Similarity from Angles (AA)
Source: NCERT Mathematics, Class 108 minute lesson
Formal statement
If in two triangles the corresponding angles are equal, the triangles are similar (AAA criterion). Since the angles of a triangle add to 180°, two pairs of equal angles are enough (AA).
The intuition
Angles fix a triangle's shape completely; only the size is left free. So matching angles is enough to prove similarity, with no measuring of sides at all.
And you only need two: if two angles match, the third must too, because all three always add to 180°.
The attention
Look at the angles. Two matching pairs settle similarity.
∠A = ∠P, ∠B = ∠Q vs AB = 4, PQ = 6
Look hereNot here
- Look here
- Matching angles. Two equal angles force the third to be equal too, and equal angles mean the same shape.
- Not here
- Side lengths. Side lengths aren't needed here. Hunting for them sends you looking for information the question doesn't give.
- What it teaches
- Use the cheapest evidence that settles the question.