Classifying Triangles
What You’ll Learn
Section titled “What You’ll Learn”In this lesson you’ll learn how to classify triangles based on the lengths of their sides and the measures of their angles.
The Concept
Section titled “The Concept”A triangle is a polygon with three sides, three vertices, and three angles. Triangles can be classified in two main ways:
By sides:
- Equilateral triangle: All three sides are equal (and all angles are 60°).
- Isosceles triangle: At least two sides are equal (and the two base angles are equal).
- Scalene triangle: All three sides have different lengths (and all angles are different).
By angles:
- Acute triangle: All three angles are less than 90°.
- Right triangle: One angle is exactly 90°.
- Obtuse triangle: One angle is greater than 90° (but less than 180°).
A triangle can belong to both categories at once (e.g., an isosceles right triangle).
Key fact: The sum of the interior angles in any triangle is always 180°.
Worked Example
Section titled “Worked Example”-
A triangle has sides of length 7 cm, 7 cm, and 10 cm.
It is isosceles (two sides equal).
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A triangle has angles measuring 50°, 60°, and 70°.
It is acute (all angles less than 90°).
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A triangle has sides 5 cm, 12 cm, and 13 cm, and one angle of 90°.
It is a right scalene triangle.
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A triangle has one angle of 120° and two sides of different lengths.
It is an obtuse scalene triangle.
Real-World Application
Section titled “Real-World Application”Triangles are everywhere in daily life:
- Roof trusses and bridges often use equilateral or isosceles triangles for strength.
- A right triangle appears in ladders leaning against walls or in corner shelves.
- Road signs (yield signs are equilateral triangles).
- When measuring land or laying out a garden, you frequently work with triangles.
- In construction and carpentry, understanding triangle types helps with stability and accurate cutting.
Recognizing triangle types helps you understand stability, design, and measurement in the real world.