Math Problem Statement

Determine the type of triangle that is drawn below.

Solution

The given triangle has the following properties:

  1. Sides: All three sides are equal (7 units each).
  2. Angles: All three angles are equal (60° each).

Determination:

This is an equilateral triangle because:

  • All sides are congruent (equal in length).
  • All interior angles are equal (each measuring 60°).

An equilateral triangle is also a type of acute triangle, as all angles are less than 90°.

Would you like a deeper explanation of equilateral triangles, their properties, or how to classify triangles in general?


Here are 5 related questions:

  1. How can you find the height of an equilateral triangle if the side length is given?
  2. What is the area of this triangle?
  3. How do equilateral triangles relate to regular polygons?
  4. Why are all equilateral triangles also acute triangles?
  5. Can you explain the symmetry properties of an equilateral triangle?

Tip: In equilateral triangles, you can use the formula Area=34×side2\text{Area} = \frac{\sqrt{3}}{4} \times \text{side}^2 for quick calculations!

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangles
Equilateral Triangles

Formulas

Area of an equilateral triangle: (√3/4) × side²
Properties of equilateral triangles: all sides are equal, all angles are 60°

Theorems

Congruence of triangles
Angle sum property of triangles
Definition of equilateral triangles

Suitable Grade Level

Grades 6-8