## How do you show an equilateral triangle?

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 are the properties of equilateral triangles?

Here are the three properties of an equilateral triangle:

• It is a regular polygon with three sides.
• All three sides are equal in length.
• All three angles are congruent and equal 60º.

What is the relationship of equilateral triangles?

In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°….

Equilateral triangle
Area
Internal angle (degrees) 60°

How can you prove that all equilateral triangles are similar?

The AAA Triangle Similarity Postulate states that if all of the angles in a triangle are equal to the corresponding angles in another triangle, then those two triangles are equal. Since every equilateral triangle’s angles are 60 degrees, every equilateral triangle is similar to one another due to this AAA Postulate.

### How are angles of an equilateral triangle related?

Since the equilateral triangle will always have three equal sides, all three of the interior angles of an equilateral triangle will equal 60 degrees (because the sum of a triangle’s interior angles is always 180 degrees) and each exterior angle in the triangle equals 120 degrees (because the sum of an exterior angle …

### What is equilateral triangle class 9?

An equilateral triangle is the one in which all the three sides are equal.

What is equilateral triangle Class 7?

Equilateral Triangle: A triangle in which all three sides are of equal length and three angles are equal. Each angle is 60°

Will equilateral triangles always be similar?

For the equilateral triangles since they always have 3 angles that are each 60° , any equilateral triangles will be similar.

## Are all equilateral octagons are similar?

So by definition, all regular polygons with the same number of sides are similar to each other. An equilateral triangle is a regular polygon with 3 sides, so all equilateral triangles are similar.

## Why are equiangular triangles equilateral?

Every equilateral triangle is also an isosceles triangle, so any two sides that are equal have equal opposite angles. Therefore, since all three sides of an equilateral triangle are equal, all three angles are equal, too. Hence, every equilateral triangle is also equiangular.

What are the properties of an equilateral triangle?

The Equilateral Triangle has 3 equal angles. The total sum of the interior angles of a triangle is 180 degrees, therefore, every angle of an equilateral triangle is 60 degrees. It is a 3 sided regular polygon. The following corollaries of equilateral triangles are derived from the properties of equilateral triangle and Isosceles triangle theorem.

How do you find the corollary of a right triangle?

In addition, a brief explanation of how the corollary is shown is attached. In a right triangle it is true that c² = a² + b², where a, b and c are the legs and the hypotenuse of the triangle respectively. Corollary 1.1

### How do you prove that a triangle is equilateral?

Theorem 2: A triangle is said to be equilateral if and only if it is equiangular. Proof: Let an equilateral triangle be ABC. AB=AC=>∠C=∠B. — (1) since angles opposite to equal sides are equal. (Isosceles triangle theorem) Also, AC=BC=>∠B=∠A — (2) since angles opposite to equal sides are equal. .

### What is every angle of an equilateral triangle?

The total sum of the interior angles of a triangle is 180 degrees, therefore, every angle of an equilateral triangle is 60 degrees. It is a 3 sided regular polygon.