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