Equilateral triangle
An equilateral triangle is a special triangle in Grade 7 geometry where all three sides are equal in length and all three angles each measure 60°. In Saxon Math, Course 2, students use this property to find perimeter (multiply one side by 3) and verify equilateral triangles from given measurements. For example, a triangle with perimeter 36 inches has sides of 36 ÷ 3 = 12 inches each. The equilateral triangle combines the Triangle Angle Sum Theorem (3 × 60° = 180°) with the properties of equal sides, making it a key building block in geometry.
Key Concepts
Property An equilateral triangle has three equal sides and three equal angles. Each angle measures $60^\circ$.
Examples A triangle with side lengths of 8 cm, 8 cm, and 8 cm is equilateral. If the perimeter of an equilateral triangle is 36 inches, each side must be $36 \div 3 = 12$ inches long. Any triangle with three $60^\circ$ angles is guaranteed to be an equilateral triangle.
Explanation Think of this as the perfectly balanced triangle! Because all the sides are the same length, the angles have to split the total $180^\circ$ equally. So each angle is always $60^\circ$.
Common Questions
What is an equilateral triangle?
An equilateral triangle has all three sides of equal length and all three angles equal to 60°. The equal angles follow from the Triangle Angle Sum Theorem: 180° ÷ 3 = 60°.
How do you find the perimeter of an equilateral triangle?
Multiply one side length by 3. For example, if each side is 8 cm, the perimeter is 8 × 3 = 24 cm.
How do you find one side length given the perimeter?
Divide the perimeter by 3. For example, if the perimeter is 36 inches, each side is 36 ÷ 3 = 12 inches.
Why does an equilateral triangle have three 60° angles?
Because all angles are equal and they must sum to 180°, each angle = 180° ÷ 3 = 60°.
Where are equilateral triangles taught in Saxon Math Course 2?
Equilateral triangles are covered in Saxon Math, Course 2, as part of Grade 7 geometry and triangle properties.
How is an equilateral triangle different from an isosceles triangle?
An isosceles triangle has at least two equal sides and two equal base angles. An equilateral triangle is a special isosceles triangle where all three sides and angles are equal.
Where do equilateral triangles appear in real life?
Yield signs, some architectural details, honeycomb patterns, and the base of many geometric constructions use equilateral triangles due to their perfect symmetry.