Concept 6.4
Reading the Correspondence
Source: NCERT Mathematics, Class 108 minute lesson
Formal statement
△ABC ~ △PQR means A ↔ P, B ↔ Q, C ↔ R. Then ∠A = ∠P, ∠B = ∠Q, ∠C = ∠R and AB/PQ = BC/QR = CA/RP. The SSS and SAS criteria also rely on matching sides in this order.
The intuition
The order of the letters is a map. The first letter matches the first letter, the second the second. Write it carelessly and you pair the wrong sides.
So AB pairs with PQ, BC with QR, CA with RP, however the triangles are drawn, rotated or flipped on the page.
The attention
Look at the order of the letters in the similarity statement.
△ABC ~ △PQR ⇒ AB ↔ PQ, not AB ↔ QR
Look hereNot here
- Look here
- The order of the letters. Position in the name decides the match: A ↔ P, B ↔ Q, C ↔ R. The sides follow: AB ↔ PQ.
- Not here
- Pairing by how the picture looks. Matching sides by how the drawing looks fails as soon as one triangle is rotated or flipped.
- What it teaches
- Let the notation carry the information. Don't re-derive it from a picture.