Remember the properties of Equilateral Triangles on the GRE

Every now and then GRE will ask questions about Equilateral Triangle.

• All sides of an equilateral triangle are equal.
• All three internal angles are equal to each other and they are always equal to 60°

Area of an equilateral triangle 

Perimeter of an equilateral triangle 

Those formulas may not be the easiest ones to remember. Sometimes it helps to understand how those formulas are worked out. Just in case if you forget!!

Example:

The above figure shows equilateral triangle . If segment  is perpendicular to and point lies on the line connecting  and , what is the value of ?

A) 

B) 

C) 

D) 

E) 

Solution:

This problem is easy provided you know what each of those terms mean and apply that knowledge.

Step 1: First we know  is an equilateral triangle. Therefore 

Step 2: Next we are told that  is perpendicular to  i.e.  must be  .

Step 3: For  sum of all internal angles must be 

Therefore . We know the values of two of these angles i.e.  and . Therefore 

A is the correct answer.