What kind of triangle has all equal sides

Another special case of an isosceles triangle is the isosceles right triangle. The height of the isosceles triangle illustrated above can be found from the Pythagorean theorem as. The mean of is given by. Considering the angle at the apex of the triangle and writing instead of , there is a surprisingly simple relationship between the area and vertex angle. As shown in the above diagram, simple trigonometry gives.

Erecting similar isosceles triangles on the edges of an initial triangle gives another triangle such that , , and concur.

The triangles are therefore perspective triangles. No set of points in the plane can determine only isosceles triangles. Gearhart, W. Weisstein, Eric W. Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. Walk through homework problems step-by-step from beginning to end. Hints help you try the next step on your own.

Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. MathWorld Book. Wolfram Web Resources ». 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 :. As regard the angles, a triangle is equiangular if all three of its angles are equal. Very early in the Elements I. From here, for a triangle, the properties of being equilateral and equiangular are equivalent, and the latter is seldom mentioned. For a polygon with the number of sides greater than 3 the equivalence no longer holds. It follows that a triangle may have at most one obtuse or even right angle.

This also follows from the Exterior Angle Theorem. If one of the angles in a triangle is obtuse, the triangle is called obtuse. A triangle with one right angle is right. Otherwise, a triangle is acute ; for all of its angles are acute.

All the definitions are naturally exclusive. There is no possible ambiguity. I came across this diagram in [ Jacobs , p. Wentworth and G. Hill Ginn, Contact Front page Contents Geometry. What is what? Triangle Classification The basic elements of any triangle are its sides and angles. 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 This applet requires Sun's Java VM 2 which your browser may perceive as a popup.

The first two are of Greek and related origins; the word "equilateral" is of Latin origin: scalene adjective : from the Indo-European root skel- "to cut. This is how the two approaches are distinguished with Venn diagrams : As regard the angles, a triangle is equiangular if all three of its angles are equal. The following diagram summarizes all possible triangle configurations.