Does there exist an equilateral triangle with rational points?

The angles examined are formed by three points with integer coordinates, two of which are on the x-axis. It turns out that the impact of that slope being rational is that it makes a 60 degree angle, with these conditions, impossible, and so no equilateral triangle exists satisfying these constraints.

Do equilateral triangles exist?

Equilateral triangle. Similar triangles do not exist in the Hyperbolic Geometry. That is because exists a relation between angles and distances given by the angle of parallelism formula. The non-existence of similar hyperbolic triangles implies the existence of a unique hyperbolic equilateral triangle fixed the angle.

Can you use Heron’s formula for equilateral triangle?

The formula shown will recalculate the area using this method. s is the length of any side of the triangle….Methods for finding triangle area.

If you know:	Use:
All 3 sides	Heron’s Formula
Two sides and included angle	Side-angle-side method

Why equilateral triangles Cannot exist?

In an equilateral triangle, all the sides are equal. If we use the longest side theorem which say in the triangle the longest side is across the largest angle. Since all the sides are equal then the angles must be equal too. So we can’t have an Right angled equilateral triangle.

What are the points of an equilateral triangle?

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 do you show that a triangle is equilateral?

A triangle is equilateral if and only if any three of the smaller triangles have either the same perimeter or the same inradius. A triangle is equilateral if and only if the circumcenters of any three of the smaller triangles have the same distance from the centroid.

Is a right triangle always equilateral?

In an equilateral triangle, the three angles are equal. Since the three angles total 180°, they are each 60°. So a right triangle is NEVER an equilateral triangle.

Is it possible to sketch a right equilateral triangle?

We know that, sum of angles in a triangle is 180∘ and the triangle to equilateral all the sides should be equal and all the corresponding angles also should be equal. So, it is not possible to draw a right angled equilateral triangle.