Properties of an Equilateral Triangle:

All three sides are of equal length.
All three angles are equal and each measures 60 degrees.
The three medians, altitudes, and angle bisectors are also all the same length.
The area of an equilateral triangle can be calculated using the formula: \( \frac{\sqrt{3}}{4} \times side^2 \)
The perimeter of an equilateral triangle is three times the length of one side.

How to Identify an Equilateral Triangle:

To identify an equilateral triangle, you can look for the following characteristics:

All sides are of the same length.
All angles are equal to 60 degrees.
Using a protractor to measure the angles, or a ruler to measure the sides can help in confirming if a triangle is equilateral.

Example Problem:

Given an equilateral triangle with a side length of 5 cm, calculate its area.

Solution:

The area of an equilateral triangle can be calculated using the formula: \( \frac{\sqrt{3}}{4} \times side^2 \)
Plugging in the given side length, Area = \( \frac{\sqrt{3}}{4} \times 5^2 \)
Area = \( \frac{\sqrt{3}}{4} \times 25 \)
Area = \( \frac{25\sqrt{3}}{4} \) cm²

Study Guide:

To study equilateral triangles, make sure to understand and practice the following:

Definition and properties of an equilateral triangle.
Formulas for calculating the area and perimeter of an equilateral triangle.
Identifying equilateral triangles based on given side lengths and angles.
Solving problems involving equilateral triangles, such as finding unknown side lengths or angles.