An equilateral triangle is a polygon with three equal sides and three equal angles. It is a special type of triangle that exhibits symmetry and has all of its sides and angles congruent to one another.
5 Must Know Facts For Your Next Test
The three angles of an equilateral triangle are all 60 degrees.
The three sides of an equilateral triangle are all of equal length.
Equilateral triangles are the most symmetric of all triangles.
The perpendicular bisectors of an equilateral triangle intersect at the center, forming three congruent 30-60-90 right triangles.
Equilateral triangles are often used in construction and design due to their stability and aesthetically pleasing properties.
Review Questions
How are the angles of an equilateral triangle related?
The three angles of an equilateral triangle are all 60 degrees. This is because an equilateral triangle has three sides of equal length, and by the properties of triangles, the sum of the three angles must be 180 degrees. Since all three angles are equal, each angle must measure 60 degrees.
Explain the relationship between the sides of an equilateral triangle and the 30-60-90 right triangles formed within it.
In an equilateral triangle, the perpendicular bisectors of the sides intersect at the center, forming three congruent 30-60-90 right triangles. This is because the three sides of an equilateral triangle are all of equal length, and the angles are all 60 degrees. When the triangle is divided by the perpendicular bisectors, the resulting right triangles have one 30-degree angle, one 60-degree angle, and one 90-degree angle, with the sides in a 1:√3:2 ratio.
Analyze how the properties of an equilateral triangle make it a desirable shape for use in construction and design.
Equilateral triangles are often used in construction and design due to their unique properties. The three equal sides and angles provide a high degree of symmetry and stability, making equilateral triangles well-suited for supporting structures and creating visually appealing designs. Additionally, the 60-degree angles allow for efficient tessellation and tiling patterns, which are commonly used in architecture and engineering. The inherent stability and aesthetic qualities of equilateral triangles make them a popular choice for a wide range of applications, from bridges and roofs to decorative elements and artistic compositions.
Related terms
Isosceles Triangle: A triangle with two equal sides and two equal angles.
Scalene Triangle: A triangle with all three sides of different lengths and all three angles of different measures.
Congruent: Figures or shapes that are exactly the same size and shape.