Lesson 3 of 10

Triangles: Angles and Sides

Triangles are the most fundamental polygon. The angle sum, triangle inequality, and special triangle types form the foundation of geometric reasoning.

Angle Sum

The three interior angles of any triangle always sum to 180°. This is the Triangle Angle Sum Theorem.

Classifying by Angles

Acute: all angles < 90°. Right: one angle = 90°. Obtuse: one angle > 90°.

Classifying by Sides

Scalene: all sides different. Isosceles: two sides equal (base angles also equal). Equilateral: all sides equal (all angles = 60°).

Triangle Inequality

The sum of any two sides must be greater than the third side. If a, b, c are sides: a+b>c, a+c>b, b+c>a.

🔬 Interactive Lab

Equilateral triangle · Angle C = 60°

✅ Check Your Understanding

Q1: A triangle has angles 40° and 75°. What is the third angle?

Q2: A triangle with two equal sides and two equal base angles is:

Q3: Can a triangle have sides of length 3, 4, and 8?

← PreviousNext Lesson →