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Quick Math Homework Help
Common Core Standard 7.G.6
Napoleon's Theorem Illustrated
A
C
B
Napoleon’s Theorem

  • Take any triangle. 
  • Draw equilateral triangles on the sides of this triangle.
  • Find the center of these three equilateral triangles.(See A,B,C)
  • Connect these three centers, and they will form an equilateral triangle

Napoleon's Theorem

Answers to example perimeter problems
Questions answered in this video..

​How do you find the perimeter of an equilateral triangle?

What is perimeter?

What is the perimeter of a equilateral triangle with sides of 12 units?

How do you find perimeter of an equilateral triangle if you only know the altitude?

​If an equilateral triangle has an altitude of 12 units,how do you find the perimeter?
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Problem 1. Find the perimeter of an equilateral triangle with a side of twelve units.








Step 1. 3*12 = 36 units

Problem 2. Find the perimeter of an equilateral triangle with an altitude of 12 units.











Step 1. Find the length of one side. The altitude creates a 30-60-90 triangle. The altitude becomes the long side of a 30-60-90 triangle. 

Step 2. In order to get the side length use                                                     
which equals 12/√3

For a review of 30-60-90 rules check here


Step 3. 12/√3 = 4√3 which is the length of half of the equilateral triangle side length

Step 4. In order to get the entire length take 2* 4√3 =8√3

Step 5. Now you can use 3 * the side length or 3* 8√3= 24√(3 ) units



equilateral triangle 30 and 60 degree angle
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s
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h
The height formula of an equilateral triangle  

Equilateral Triangle Practice Problems

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altitude formula equilateral triangle
area formula equilateral triangle
equilateral triangle 12 unit side

Properties of an Equilateral Triangle?

The perimeter formula of an equilateral triangle 
equilateral triangle height of 12
long side 30 30 90 triangle/square root 3
Properties of an equilateral triangle
s = side length
The area of an equilateral triangle 

Equilateral Triangle Formulas

Equilateral Triangle Properties

Types of Triangles

​All three sides are congruent. Congruent just means they are equal.
All three angles are also congruent, which is also called equiangular.
The angles in an equilateral triangle add to 180 degrees and the angles are congruent, therefore the angle measure equals 60 degrees.
3* s 
Triangles have three sides and three angles, but what is an equilateral triangle? In Euclidean Geometry the specifics of an equilateral triangle are as follows.
equilateral triangle congruent angles/what is an equilateral triangle?
60
60
60
equilateral triangle congruent sides/what is an equilateral triangle?
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s = side length
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equilateral triangle 30 and 60 degree angle
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Hi Welcome to MooMooMath. Today we are going to look at Equilateral Triangles. I have drawn two different triangles. The first one we know is equilateral because all three sides are marked congruent. You might see a congruent symbol, (points to triangle) or you might see that the measure of each side is equal. There are two ways to show that the different sides are equal. On the second one let’s look at it in perspective of the actual measure of the angles. We know that a triangle adds up to 180 degrees. So if we have three equal angles we are going to take that and divide it by three. One hundred and eighty divided by three is equal to sixty. Therefore, each of these angles have to measure 60 degrees. If the three angles measure 60 then it is an equilateral triangle. So let’s look at the rules. The first rule is that all three sides of the triangle are congruent which just means they are equal. Second, all three angles have to be congruent.Finally, the measure of the angles will always be 60 degrees. Hope this video was helpful.