What is the equilateral triangle theorem?

What is the equilateral triangle theorem?

Napoleon’s theorem states that if three equilateral triangles are drawn on the legs of any triangle (either all drawn inwards or outwards) and the centers of these triangles are connected, the result is another equilateral triangle.

Do triangles have vectors?

Finding unknown quantities in triangles, such as the lengths of sides and the measure of angles, is a critical portion of the study of trigonometry. Vectors are a way to describe these kinds of quantities; they have both a magnitude and a direction.

How do you find the vector form of a triangle?

The conditions for three vectors to form a triangle are:

1. The sum of magnitudes of any two of them must be greater than the magnitude of third.
2. magnitude of sum of two vectors must be equal to the magnitude of third.
3. All three should have different directions.

How do you prove that a triangle is equilateral?

Answer: If three sides of a triangle are equal and the measure of all three angles is equal to 60 degrees then the triangle is an equilateral triangle. The distance formula can be used to prove that a triangle is an equilateral triangle.

What is special about an equilateral triangle?

An equilateral triangle is a triangle whose sides are all equal. It is a specific kind of isosceles triangle whose base is equal to each leg, and whose vertex angle is equal to its base angles. Therefore, since all three sides of an equilateral triangle are equal, all three angles are equal, too.

How many vectors are in a triangle?

We can make a triangle out of the two vectors and , and a third vector − (see lesson 1 on vectors 1). Look at the diagram below.

How many vectors are there in a triangle?

What are the properties of equilateral triangle?

Properties of an Equilateral Triangle

• Three sides are equal.
• Three angles are equal i.e 60° each.
• A regular polygon having three equal sides.
• Median, angle bisector and altitude are all equal in an equilateral triangle.
• The dividing perpendicular from the angle of the vertex is parted into two equal halves i.e. 30°.