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Mid-Point and Its Converse

ICSE · Class 9 · Mathematics

Complete topic list for Mid-Point and Its Converse in ICSE Class 9 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

34 questions25 flashcards5 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

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

Frequently Asked Questions

What are the important topics in Mid-Point and Its Converse for ICSE Class 9 Mathematics?
Mid-Point and Its Converse covers several key topics that are frequently asked in ICSE Class 9 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Mid-Point and Its Converse — ICSE Class 9 Mathematics?
Understand the core concepts first, then work through the 34 practice questions available for this chapter. Revise formulas and 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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