Triangles
Types, properties, and theorems
lessons (3)
Types of Triangles
Learn to identify and classify triangles by their sides and angles.
Pythagorean Theorem
Learn the famous relationship between the sides of a right triangle and use it to solve real-world problems.
Triangle Angle Sum
Discover why the three angles in any triangle always add up to 180 degrees.
Triangles are the simplest polygons and the building blocks of all geometry. Every polygon can be divided into triangles, and triangle properties underlie architecture, engineering, and design. From the Pythagorean theorem to trigonometry, triangles are central to mathematics.
In this topic, you will classify triangles by sides (equilateral, isosceles, scalene) and angles (acute, right, obtuse). You will learn the angle sum property, triangle inequality, and relationships between sides and angles. The Pythagorean theorem connects the sides of right triangles in one of mathematics most famous formulas.
Our lessons bring triangles to life through real-world applications in construction, navigation, and art. With interactive visualizations, you will develop deep geometric intuition about these fundamental shapes.
What Students Will Learn
- Classify triangles by sides and angles
- Apply the triangle angle sum theorem (180°)
- Use the triangle inequality theorem
- Calculate area using base and height
- Apply the Pythagorean theorem for right triangles
- Find missing sides and angles
- Solve real-world problems involving triangles
Frequently Asked Questions
Why do triangle angles always sum to 180°?
Draw a line through one vertex parallel to the opposite side. The three angles of the triangle equal the angles on a straight line. Since a straight angle is 180°, the triangle angles must sum to 180°.
What is the triangle inequality?
The sum of any two sides must be greater than the third side. This is why you cannot make a triangle with sides 1, 2, and 10—the two shorter sides cannot reach to connect.
When can I use the Pythagorean theorem?
Only for right triangles! If a triangle has a 90° angle, then a² + b² = c², where c is the hypotenuse (longest side, opposite the right angle) and a, b are the legs.