An isosceles triangle is a triangle with (at least) two equal sides. In the figure above, the two equal sides have length
A triangle with all sides equal is called an equilateral triangle, and a triangle with no sides equal is called a scalene triangle. An equilateral triangle is therefore a special case of an isosceles triangle having not just two, but all three sides and angles equal. 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 area is therefore given by
The inradius of an isosceles triangle is given by
The mean of
so the geometric centroid is
or 2/3 the way from its vertex (Gearhart and Schulz 1990).
Considering the angle at the apex of the triangle and writing
so the area is
Erecting similar isosceles triangles on the edges of an initial triangle
No set of
30-60-90 Triangle, Acute Triangle, Equilateral Triangle, Golden Gnomon, Golden Triangle, Isosceles Right Triangle, Isosceles Tetrahedron, Isoscelizer, Kiepert Parabola, Obtuse Triangle, Petr-Neumann-Douglas Theorem, Point Picking, Pons Asinorum, Right Triangle, Scalene Triangle, Steiner-Lehmus Theorem Explore this topic in the MathWorld classroom Gearhart, W. B. and Schulz, H. S. "The Function
Weisstein, Eric W. "Isosceles Triangle." From MathWorld--A Wolfram Web Resource. //mathworld.wolfram.com/IsoscelesTriangle.html