source: ncert
topic: geometry
class_level: class_7
chapter: ch7
difficulty: beginner
Class 7 | Ch7: Congruence of Triangles Congruent: same shape AND same size. Symbol: congruent to. ORDER MATTERS: triangle ABC congruent to triangle PQR means A-P, B-Q, C-R. Rules: SSS(all 3 sides), SAS(2 sides+INCLUDED angle), ASA(2 angles+INCLUDED side), AAS(2 angles+non-included side), RHS(right angle+hypotenuse+one side). AAA: gives SIMILAR triangles not congruent (same shape, different size). SSA: FAILS - ambiguous case (two possible triangles). CPCT: Corresponding Parts of Congruent Triangles are equal (used AFTER proving congruence). Isosceles proof: AB=AC. Draw altitude AD. Triangles ABD and ACD congruent by RHS. Angle B=angle C by CPCT. SAS: angle must be INCLUDED between the two sides. ASA: side must be INCLUDED between two angles.