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Syllabus

Mid-Point and Its Converse — Syllabus

ICSE · Class 9 · Mathematics

What Mid-Point and Its Converse covers in ICSE Class 9 Mathematics: 4 topics, for the 2026-27 session. Part of the ICSE Class 9 Mathematics syllabus.

34 questions25 flashcards5 formulas & key relations5 concepts

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A step-by-step visual proof of the Mid-Point Theorem, showing a triangle ABC with D and E as mid-points of AB and AC respectively. Construction involves drawing CF parallel to BA, extending DE to F, a
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4 Topics · ICSE Class 9 Mathematics · 2026-27

Topics in Mid-Point and Its Converse

1

1. Mid-Point Theorem

  • The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and equal to half of it.
  • In triangle ABC, D and E are the mid-points of sides AB and AC respectively.
  • The construction in the proof draws CF parallel to BA and meeting DE produced at F.
2

2. Converse of Mid-Point Theorem

  • The straight line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side.
  • In triangle ABC, D is the mid-point of AB and DE is drawn parallel to BC.
  • The conclusion is that E is the mid-point of AC, so AE = EC.
3

3. Applications of the Mid-Point Theorem

  • Joining the mid-points of the adjacent sides of a quadrilateral gives a parallelogram.
  • In quadrilateral ABCD, P, Q, R, S are the mid-points of AB, BC, CD, DA.
  • In triangle ABD, PS is parallel to BD and PS equals half of BD.
4

4. Equal Intercept Theorem and Its Use

  • If a transversal makes equal intercepts on three or more parallel lines, then any other line cutting them will also make equal intercepts.
  • In the theorem, transversal AB makes equal intercepts PQ = QR on three parallel lines l, m, and n.
  • Another transversal CD cuts the same three parallel lines and makes intercepts LM and MN.

Key Concepts

Central concept: Relationships created by joining mid-points in triangles, quadrilaterals, and trapeziums, and the equal intercept property on parallel lines

Mid-Point TheoremConverse of Mid-Point TheoremEqual Intercept TheoremQuadrilateral midpoint figureParallelogram applicationsRight triangle applicationMedian extension applicationTrapezium mid-segment

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Frequently Asked Questions

What are the important topics in Mid-Point and Its Converse for ICSE Class 9 Mathematics?
Key topics in Mid-Point and Its Converse include Mid-Point Theorem, Converse of Mid-Point Theorem, Applications of the Mid-Point Theorem, Equal Intercept Theorem and Its Use. Study these first, then practise questions on each for Class 9 exams.
How should I revise Mid-Point and Its Converse for Class 9 exams?
Learn the core ideas first, then work through the 34 practice questions on Mid-Point and Its Converse. 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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