Class 10 · Chapter 6
Triangles
Similar triangles, criteria for similarity (AAA, SAS, SSS), Basic Proportionality Theorem (Thales) and Pythagoras theorem.
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Detailed theory
Two figures are similar if they have the same shape (but not necessarily the same size). For triangles, this means all pairs of corresponding angles are equal and all pairs of corresponding sides are proportional. The common ratio of corresponding sides is called the scale factor.
Key concepts & formulas
01
Two triangles are similar iff corresponding angles are equal and corresponding sides are in the same ratio.
02
BPT (Thales): a line parallel to one side of a triangle divides the other two sides proportionally.
03
Areas of similar triangles are proportional to the square of any pair of corresponding sides.
04
Pythagoras: in a right-angled triangle, .
05
Converse of Pythagoras: if , the triangle is right-angled.
06
Similarity criteria: AAA (or AA), SSS ratio, SAS ratio.