Isosceles Triangles
ICSE · Class 9 · Mathematics
Quick revision notes for Isosceles Triangles — ICSE Class 9 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Basic Definitions and Introduction
- An isosceles triangle has at least two equal sides
- An equilateral triangle is a special case of isosceles triangle where all three sides are equal
- In an isosceles triangle, the equal sides are called arms and the third side is called the base
Theorem 1: Equal Sides → Equal Angles
- If two sides of a triangle are equal, then angles opposite to them are also equal
- This is the fundamental property of isosceles triangles
- Proof uses construction of perpendicular from vertex to base
Theorem 2: Equal Angles → Equal Sides
- If two angles of a triangle are equal, then sides opposite to them are also equal
- This is the converse of Theorem 1
- Proof uses construction of perpendicular from vertex to base
Properties and Important Results
- The angle bisector from vertex of isosceles triangle bisects the base at right angles
- The perpendicular bisector of base passes through the vertex
- The line joining midpoint of base to vertex is perpendicular to base and bisects vertex angle
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