Triangles are three-sided polygons, and they can be classified based on different criteria, such as the lengths of their sides and the measures of their angles. Here are the main types of triangles:
Based on Side Lengths
1. Equilateral Triangle: Definition: All three sides are of equal length.
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| Equilateral Triangle |
Properties: All three angles are also equal, each measuring 60 degrees.
2. Isosceles Triangle: Definition: At least two sides are of equal length.
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| Isosceles Triangle |
Properties: The angles opposite the equal sides are equal.
3. Scalene Triangle: Definition: All three sides have different lengths.
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| Scalene Triangle |
Properties: All three angles can have different measures.
Based on Angle Measures
1. Acute Triangle: Definition: All angles are less than 90 degrees.
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| Acute Triangle |
2. Obtuse Triangle: Definition: One angle is greater than 90 degrees.
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| Obtuse Triangle |
3. Right Triangle: Definition: One angle is exactly 90 degrees.
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| Right Triangle |
Properties: The side opposite the right angle is called the hypotenuse.
Based on a Combination of Sides and Angles
1. Right-angled Isosceles Triangle: Definition: A triangle with one angle measuring 90 degrees and two equal sides.
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| Right-angled Isosceles Triangle |
Properties: The side opposite the right angle is the hypotenuse, and the other two sides are equal.
2. Equiangular Triangle: Definition: All three angles are equal.
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| Equiangular Triangle |
Properties: It is also an equilateral triangle, with all three sides of equal length.
Based on the Sum of Angles
The sum of the interior angles of any triangle is always 180 degrees.
Conclusion
Understanding these classifications helps in solving various problems in geometry and trigonometry. It's important to note that these categories are not mutually exclusive; a triangle can belong to more than one category. For example, an equilateral triangle is also an acute triangle and an equiangular triangle.