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Revision Notes

Area Theorems — Revision Notes

ICSE · Class 9 · Mathematics

Area Theorems revision notes for ICSE Class 9 Mathematics: 4 topics in quick points. Part of the ICSE Class 9 Mathematics syllabus.

35 questions25 flashcards3 formulas & key relations5 concepts

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An infographic showing the basic area formulas for a triangle, rectangle, and parallelogram, as a refresher before introducing area theorems.
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Key Topics to Revise

1

1. Basic ideas and figures between the same parallels

  • Area of a plane figure is the region bounded by it.
  • Figures with bases on one straight line and their other vertices on another line parallel to it are between the same parallels.
  • Such figures have equal altitude or height.
2

2. Theorem 19 and its corollary

  • Parallelograms on the same base and between the same parallels are equal in area.
  • In the proof, opposite sides of parallelogram ABCD are equal, so triangles ADF and BCE are congruent by ASA.
  • Congruent triangles are equal in area.
3

3. Theorem 20: area of a triangle and a parallelogram

  • The area of a triangle is half that of a parallelogram on the same base and between the same parallels.
  • In the proof, a parallelogram is constructed so that the given triangle has the same base and the same height as the parallelogram.
  • A diagonal of a parallelogram divides it into two equal-area triangles.
4

4. Theorem 21 and corollaries

  • Triangles on the same base and between the same parallels are equal in area.
  • In the proof, two parallelograms are constructed on the two triangles and their areas are shown equal using Theorem 19.
  • Each triangle is half of its constructed parallelogram.

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Full Notes

Key Concepts

Equal figures are figures with equalIf the bases of figures lieParallelograms on the same baseSince a rectangle is alsoThe area of a triangle

Frequently Asked Questions

What are the important topics in Area Theorems for ICSE Class 9 Mathematics?
Key topics in Area Theorems include Basic ideas and figures between the same parallels, Theorem 19 and its corollary, Theorem 20: area of a triangle and a parallelogram, Theorem 21 and corollaries. Study these first, then practise questions on each for Class 9 exams.
How should I revise Area Theorems for Class 9 exams?
Learn the core ideas first, then work through the 35 practice questions on Area Theorems. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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All ICSE Class 9 Mathematics Revision Notes

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