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Revision Notes

Isosceles Triangles — Revision Notes

ICSE · Class 9 · Mathematics

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

35 questions20 flashcards8 formulas & key relations5 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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Key Topics to Revise

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.

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Full Notes

Key Concepts

A triangleIf all the sides ofIf two sides of a triangleIf two angles of a triangleIn an isosceles triangle

Frequently Asked Questions

What are the important topics in Isosceles Triangles for ICSE Class 9 Mathematics?
Key topics in Isosceles Triangles include Core ideas and definitions, Important theorem proofs, Other properties of isosceles triangles, Solved problem patterns to remember. Study these first, then practise questions on each for Class 9 exams.
How should I revise Isosceles Triangles for Class 9 exams?
Learn the core ideas first, then work through the 35 practice questions on Isosceles Triangles. 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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