📐 Classification by Sides

Equilateral Triangle:

• All three sides are equal in length

• All three angles are equal (60° each)

• Symbol: Use tick marks to show equal sides

Isosceles Triangle:

• Two sides are equal in length

• Two angles are equal (called base angles)

• The equal sides are called legs, the third side is the base

Scalene Triangle:

• All three sides are different lengths

• All three angles are different sizes

• No lines of symmetry

📏 Classification by Angles

Acute Triangle:

• All three angles are less than 90°

• All angles are acute angles

• The triangle appears "sharp" or "pointed"

Right Triangle:

• One angle is exactly 90° (right angle)

• The other two angles are acute and add up to 90°

• The side opposite the right angle is called the hypotenuse

Obtuse Triangle:

• One angle is greater than 90° (obtuse angle)

• The other two angles are acute

• The triangle appears "wide" or "flat"

📝 Important Properties & Rules

Triangle Inequality Principle:

• The sum of any two sides must be greater than the third side

• If a, b, and c are the sides: a + b > c, a + c > b, b + c > a

Angle Sum Property:

• The sum of all angles in any triangle is always 180°

Geometric Notation:

• Triangles are named using three vertices: △ABC

• Angles are written as ∠A, ∠B, ∠C

• Sides are written as AB, BC, AC (or a, b, c)

Side-Angle Relationships:

• The longest side is opposite the largest angle

• The shortest side is opposite the smallest angle

• In an isosceles triangle, equal sides are opposite equal angles