Start by imagining a slice of pizza: it’s shaped like a triangle! Triangles are everywhere, from the pyramids to the simplest roof structures. Let’s dive into understanding what makes triangles unique and their different types.
Contents
Click any of the elements in the outline below to jump to a specific part of the page.
- What is a Triangle?
- Types of Triangles by Sides
- Types of Triangles by Angles
- Properties of Triangles
- Quiz: Test Your Knowledge
- Key Takeaways
- Watch: The Triangle Song
What is a Triangle?
A triangle is a polygon with three sides, three angles, and three vertices. It is one of the most fundamental shapes in geometry.
Definition: A triangle is a closed figure formed by three line segments that intersect at three vertices.
Key Characteristics
- Sides: The line segments that form the triangle.
- Vertices: The points where the sides meet.
- Angles: The spaces between the sides.
Types of Triangles by Sides
Equilateral Triangle
- All three sides are of equal length.
- All three angles are equal and measure 60°.
Example: A perfectly balanced triangle, often used in construction for stability.
Isosceles Triangle
- Two sides are of equal length.
- Two angles opposite the equal sides are also equal.
Example: The roof of many houses forms an isosceles triangle.
Scalene Triangle
- All three sides are of different lengths.
- All three angles are different.
Example: A triangular slice of land with uneven borders.
Types of Triangles by Angles
Acute Triangle
- All three angles are less than 90°.
Tip: Think of sharp angles that point inward.
Right Triangle
- One angle is exactly 90°.
- The side opposite the right angle is called the hypotenuse.
Example: Right triangles are essential in construction and navigation.
Obtuse Triangle
- One angle is greater than 90°.
Note: The largest angle always determines the type.
Properties of Triangles
- The sum of the interior angles of any triangle is always 180°.
- The length of any side must be less than the sum of the other two sides.
- Triangles are the simplest polygons and are incredibly stable structures.
Quiz: Test Your Knowledge
Key Takeaways
- Triangles are three-sided polygons with three angles.
- Triangles are classified by sides (equilateral, isosceles, scalene) and angles (acute, right, obtuse).
- The sum of a triangle’s interior angles is always 180°.
- Understanding triangles is fundamental for both geometry and practical applications in the real world.
Watch: The Triangle Song
To help you remember the types of triangles, check out this catchy song!