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A triangle in which all three sides are of equal lengths is called _________.
- a)Scalene
- b)Isosceles
- c)Equilateral
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A triangle in which all three sides are of equal lengths is called ___...
A triangle in which all three sides are of equal lengths is called Equilateral Triangle.
Most Upvoted Answer
A triangle in which all three sides are of equal lengths is called ___...
Equilateral Triangle: A Triangle with Equal Length Sides
An equilateral triangle is a specific type of triangle where all three sides are of equal lengths. It is a fundamental concept in geometry and is classified as a special case of triangles based on its side lengths.
Definition:
- An equilateral triangle is a polygon with three sides of equal lengths.
- Each internal angle of an equilateral triangle measures 60 degrees.
Key Points:
1. Equal Side Lengths: In an equilateral triangle, all three sides have the same length. This characteristic distinguishes it from other types of triangles.
2. Symmetry: Due to its equal side lengths, an equilateral triangle possesses symmetry. It can be folded along any of its medians, resulting in all three sides overlapping perfectly.
3. Regular Polygon: An equilateral triangle is the simplest form of a regular polygon. Regular polygons have all sides and angles equal.
4. Interior Angles: The interior angles of an equilateral triangle are all equal to 60 degrees. This means that when the angles are added together, they sum up to 180 degrees.
5. Exterior Angles: The exterior angles of an equilateral triangle are each equal to 120 degrees. The exterior angle is the supplementary angle to the interior angle.
Usage and Application:
- Equilateral triangles are used in various fields of study, including mathematics, art, and engineering.
- In mathematics, equilateral triangles serve as a basis for understanding geometric principles and properties.
- In art, equilateral triangles are often used to create symmetrical and balanced compositions.
- In engineering and architecture, equilateral triangles can be utilized to create stable and strong structures.
In conclusion, an equilateral triangle is a special type of triangle where all three sides are of equal lengths. It possesses symmetry, has interior angles measuring 60 degrees each, and is a fundamental concept in geometry. Understanding the properties and characteristics of an equilateral triangle is important in various fields of study and practical applications.
An equilateral triangle is a specific type of triangle where all three sides are of equal lengths. It is a fundamental concept in geometry and is classified as a special case of triangles based on its side lengths.
Definition:
- An equilateral triangle is a polygon with three sides of equal lengths.
- Each internal angle of an equilateral triangle measures 60 degrees.
Key Points:
1. Equal Side Lengths: In an equilateral triangle, all three sides have the same length. This characteristic distinguishes it from other types of triangles.
2. Symmetry: Due to its equal side lengths, an equilateral triangle possesses symmetry. It can be folded along any of its medians, resulting in all three sides overlapping perfectly.
3. Regular Polygon: An equilateral triangle is the simplest form of a regular polygon. Regular polygons have all sides and angles equal.
4. Interior Angles: The interior angles of an equilateral triangle are all equal to 60 degrees. This means that when the angles are added together, they sum up to 180 degrees.
5. Exterior Angles: The exterior angles of an equilateral triangle are each equal to 120 degrees. The exterior angle is the supplementary angle to the interior angle.
Usage and Application:
- Equilateral triangles are used in various fields of study, including mathematics, art, and engineering.
- In mathematics, equilateral triangles serve as a basis for understanding geometric principles and properties.
- In art, equilateral triangles are often used to create symmetrical and balanced compositions.
- In engineering and architecture, equilateral triangles can be utilized to create stable and strong structures.
In conclusion, an equilateral triangle is a special type of triangle where all three sides are of equal lengths. It possesses symmetry, has interior angles measuring 60 degrees each, and is a fundamental concept in geometry. Understanding the properties and characteristics of an equilateral triangle is important in various fields of study and practical applications.
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A triangle in which all three sides are of equal lengths is called ___...
Equilateral Triangle
An equilateral triangle is a type of triangle in which all three sides are of equal lengths. It is a special case of a regular polygon, where all sides and angles are equal. In an equilateral triangle, all three angles are also equal to 60 degrees.
Characteristics of an Equilateral Triangle
- All three sides of an equilateral triangle are of equal length.
- All three angles of an equilateral triangle are equal to 60 degrees.
- The sum of the interior angles of an equilateral triangle is always 180 degrees.
- The altitude, median, and perpendicular bisectors of an equilateral triangle are concurrent.
- The circumcenter, incenter, and centroid of an equilateral triangle coincide and are the same point.
- The area of an equilateral triangle can be calculated using various formulas, such as A = (s^2 * √3) / 4, where s is the length of a side.
Visual Representation
To visualize an equilateral triangle, imagine a triangle with all three sides of equal length. Each angle of the triangle measures 60 degrees. It appears symmetrical and balanced.
Distinguishing from Other Types of Triangles
- Scalene Triangle: In a scalene triangle, all three sides have different lengths. Therefore, it is not an equilateral triangle.
- Isosceles Triangle: In an isosceles triangle, two sides have the same length, while the third side is of a different length. Since all three sides of an equilateral triangle are equal, it is not an isosceles triangle either.
Importance of Equilateral Triangles
- Equilateral triangles are commonly used in architecture and engineering because of their symmetry and stability.
- They are often found in the design of bridges, buildings, and other structures.
- The properties of equilateral triangles are used in various mathematical and geometrical calculations.
- They are also used in various puzzles and games.
Conclusion
An equilateral triangle is a special type of triangle in which all three sides are of equal lengths. It possesses unique properties and characteristics that distinguish it from other types of triangles. Equilateral triangles have practical applications in various fields and are important in mathematical and geometrical concepts.
An equilateral triangle is a type of triangle in which all three sides are of equal lengths. It is a special case of a regular polygon, where all sides and angles are equal. In an equilateral triangle, all three angles are also equal to 60 degrees.
Characteristics of an Equilateral Triangle
- All three sides of an equilateral triangle are of equal length.
- All three angles of an equilateral triangle are equal to 60 degrees.
- The sum of the interior angles of an equilateral triangle is always 180 degrees.
- The altitude, median, and perpendicular bisectors of an equilateral triangle are concurrent.
- The circumcenter, incenter, and centroid of an equilateral triangle coincide and are the same point.
- The area of an equilateral triangle can be calculated using various formulas, such as A = (s^2 * √3) / 4, where s is the length of a side.
Visual Representation
To visualize an equilateral triangle, imagine a triangle with all three sides of equal length. Each angle of the triangle measures 60 degrees. It appears symmetrical and balanced.
Distinguishing from Other Types of Triangles
- Scalene Triangle: In a scalene triangle, all three sides have different lengths. Therefore, it is not an equilateral triangle.
- Isosceles Triangle: In an isosceles triangle, two sides have the same length, while the third side is of a different length. Since all three sides of an equilateral triangle are equal, it is not an isosceles triangle either.
Importance of Equilateral Triangles
- Equilateral triangles are commonly used in architecture and engineering because of their symmetry and stability.
- They are often found in the design of bridges, buildings, and other structures.
- The properties of equilateral triangles are used in various mathematical and geometrical calculations.
- They are also used in various puzzles and games.
Conclusion
An equilateral triangle is a special type of triangle in which all three sides are of equal lengths. It possesses unique properties and characteristics that distinguish it from other types of triangles. Equilateral triangles have practical applications in various fields and are important in mathematical and geometrical concepts.
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A triangle in which all three sides are of equal lengths is called _________.a)Scaleneb)Isoscelesc)Equilaterald)None of theseCorrect answer is option 'C'. Can you explain this answer?
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