| --- |
| source: ncert |
| topic: geometry |
| class_level: class_7 |
| chapter: ch7 |
| difficulty: beginner |
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| |
| 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. |
