# What is the relationship between acute and equilateral triangles

### Triangle Classification What's the difference between equilateral, isosceles, and scalene triangles? How about obtuse, right, and little acute ones? Relationships. Learn what acute and obtuse triangles are, their properties, and key formulas An obtuse triangle may be either isosceles (two equal sides and two One of the sides of this square coincides with a part of the longest side of the triangle. then the following relation for altitude is true for an obtuse triangle. In a equilateral triangle, all the angles are equal. All the angles in a triangle sum up to o. We can determine the angles by dividing by 3.

Equilateral triangles are the only triangles whose Steiner inellipse is a circle specifically, it is the incircle. The integer-sided equilateral triangle is the only triangle with integer sides and three rational angles as measured in degrees.

Equilateral triangles are found in many other geometric constructs. The intersection of circles whose centers are a radius width apart is a pair of equilateral arches, each of which can be inscribed with an equilateral triangle. They form faces of regular and uniform polyhedra. Three of the five Platonic solids are composed of equilateral triangles. In particular, the regular tetrahedron has four equilateral triangles for faces and can be considered the three-dimensional analogue of the shape.

### Types of Triangles - MathBitsNotebook (Geo - CCSS Math)

The plane can be tiled using equilateral triangles giving the triangular tiling. Geometric construction[ edit ] Construction of equilateral triangle with compass and straightedge An equilateral triangle is easily constructed using a straightedge and compassbecause 3 is a Fermat prime. Draw a straight line, and place the point of the compass on one end of the line, and swing an arc from that point to the other point of the line segment.

Triangles are classified depending on relative sizes of their elements. As regard their sides, triangles may be Scalene all sides are different Isosceles two sides are equal Equilateral all three sides are equal And as regard their angles, triangles may be Acute all angles are acute Right one angle is right Obtuse one angle is obtuse Equiangular all angles are equal A triangle is scalene if all of its three sides are different in which case, the three angles are also different.

• What is the difference between an equilateral triangle and an isosceles triangle?
• Why are all equilateral triangles acute?
• Equilateral triangle

If two of its sides are equal, a triangle is called isosceles. A triangle with all three equal sides is called equilateral.

## Triangle Classification

Schwartzman's The Words of Mathematics explain the etymology the origins of the words. The first two are of Greek and related origins; the word "equilateral" is of Latin origin: A scalene triangle is uneven in the sense that all three sides are of different lengths. The scalene muscles on each side of a person's neck are named for their triangular appearance. A scalene cone or cylinder is one whose axis is not perpendicular to its base; opposite elements make "uneven" angles with the base.

### What is the difference between an equilateral triangle and an isosceles triangle? | Socratic

The Indo-European root s kel- "curved, bent" is found in scoliosis and colon, borrowed from Greek. In geometry, an isosceles triangle or trapezoid has two equal legs. It may seem strange that the root means "bent" even though the sides of a triangle or trapezoid are straight, but each leg is bent relative to the adjoining legs.

Related borrowings from Latin are bilateral and multilateral. In geometry, equilateral triangle is one in which all sides are equal in length.

This is how the two approaches are distinguished with Venn diagrams: 