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Isosceles Triangles

ICSE · Class 9 · Mathematics

Complete topic list for Isosceles Triangles in ICSE Class 9 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

35 questions20 flashcards5 concepts

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A labeled diagram illustrating an isosceles triangle with two equal sides and the angles opposite to them also being equal. Includes the definition of an equilateral triangle as a special case.
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4 Topics · ICSE Class 9 Mathematics

Topics in Isosceles Triangles

1

Core ideas and definitions

  • An isosceles triangle has at least two equal sides.
  • An equilateral triangle has all three sides equal.
  • An equilateral triangle satisfies all the properties of an isosceles triangle.
2

Important theorem proofs

  • Theorem 1 uses AD perpendicular to BC.
  • In Theorem 1, angle ADB = angle ADC = 90° because AD is perpendicular to BC.
  • In Theorem 1, AB = AC, AD = AD, and angle ADB = angle ADC.
3

Other properties of isosceles triangles

  • The bisector of the angle at the vertex of an isosceles triangle bisects the base at right angles.
  • If equal sides of an isosceles triangle are produced, the exterior angles so formed are equal.
  • The perpendicular bisector of the base of an isosceles triangle passes through the vertex of the triangle.
4

Solved problem patterns to remember

  • In the problem with AB = AC and DB = DC, triangles ABD and ACD are congruent by S.S.S., so DA bisects BC at right angles and angle ABD = angle ACD.
  • In the problem with BO and CO as angle bisectors in triangle ABC where AB = AC, first prove OB = OC from triangle BOC, then use S.A.S. to prove triangle AOB congruent to triangle AOC, showing AO bisec
  • In the problem with D and E as mid-points of equal sides AB and AC, one method proves triangle ABE congruent to triangle ACD and gives BE = CD.

Key Concepts

Central concept: Isosceles Triangle

DefinitionRelationship with equilateral triangleTheorem 1Theorem 2Properties to proveSolved Problem 2Solved Problem 3Solved Problem 4

Frequently Asked Questions

What are the important topics in Isosceles Triangles for ICSE Class 9 Mathematics?
Isosceles Triangles 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 Isosceles Triangles — ICSE Class 9 Mathematics?
Understand the core concepts first, then work through the 35 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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All 28 chapters — ICSE Class 9 Mathematics Syllabus

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