Area Theorems
ICSE · Class 9 · Mathematics
Quick revision notes for Area Theorems — ICSE Class 9 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
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Basic Concepts and Definitions
- Area of a plane figure is the region bounded by it
- Equal figures mean figures equal in area
- Congruent figures are always equal in area, but equal figures may not be congruent
Theorem 19: Parallelograms on Same Base and Between Same Parallels
- Parallelograms on the same base and between same parallels are equal in area
- This theorem applies to all types of parallelograms including rectangles
- The proof uses congruent triangles (ASA criterion)
Theorem 20: Triangle Area Half of Parallelogram
- Area of triangle is half the area of parallelogram on same base and between same parallels
- Diagonal of parallelogram divides it into two equal triangles
- This theorem connects triangle and parallelogram areas
Theorem 21: Triangles on Same Base and Between Same Parallels
- Triangles on same base and between same parallels are equal in area
- Proof involves constructing parallelograms and using previous theorems
- This is the triangle version of Theorem 19
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