The two equal sides of an isosceles triangle are called the legs of the triangle, and the third side the base. The vertex between the legs is called the apex, and the angle at the apex is called the apical angle. The other two angles are called the base angles.
Theorems of isosceles triangles
The base angles of an isosceles triangle are equal.
The median from the apex of an isosceles triangle is also an altitude, a right bisector and an angle bisector
Equilateral triangles
Theorems of equilateral triangles
All interior angles of an equilateral triangle are \(60^\circ\).
The centroid of an equilateral triangle coincides with its orthocentre, circumcentre and incentre.
Right triangles
The two sides that form the right angle are called the legs of the triangle, and the third side the hypotenuse.
Theorems of right triangles
Pythagorean theorem. The area of the square constructed on the hypotenuse of a right triangle is equal to the sum of the areas of the squares constructed on the legs of the triangle.
\[c^2=a^2+b^2\]
Therefore, the hypotenuse of a right triangle is its longest side.
The orthocentre of a right triangle is at the vertex of the right angle.
The circumcentre of a right triangle is at the midpoint of the hypotenuse.
