Chapter 6 Triangles

Notes

Triangles:

Triangle = closed figure with 3 sides Sum of angles of triangle = 180°

Types of triangles:

By sides:

Equilateral Isosceles Scalene

By angles:

Acute Right angled Obtuse

Similar triangles:

Same shape Angles equal Sides proportional

Similarity criteria:

AAA All corresponding angles equal SAS Two sides proportional and included angle equal SSS All corresponding sides proportional

Basic Proportionality Theorem (BPT):

If a line is parallel to one side of triangle, it divides other two sides in same ratio

Pythagoras theorem:

Hypotenuse² = Base² + Perpendicular²

Converse of Pythagoras theorem:

If square of longest side equals sum of squares of other sides, triangle is right angled

Area theorem:

Ratio of areas of similar triangles = square of ratio of corresponding sides

Important formulas:

c² = a² + b² Area ratio = (side ratio)²

Common mistakes:

Wrong side matching Forgetting square in area ratio Incorrect ratio writing Using hypotenuse wrongly