Golden triangle (mathematics) Golden triangle (mathematics) A golden triangle, also known as the sublime triangle,is an isosceles triangle in which the duplicated side is in the golden ratio to the distinct side: Golden triangles are found in the nets of several stellations of dodecahedrons and icosahedrons. Also, it is the shape of the triangles found in the points of pentagrams. The vertex angle is equal to Since the angles of a triangle sum to 180°, base angles are therefore 72° each. The golden triangle can also be found in a regular decagon, or an equiangular and equilateral ten-sided polygon, by connecting any two
Triangle it; this is the exterior angle theorem. The sum of the measures of the three exterior angles (one for each vertex) of any triangle is 360 degrees. Two triangles are said to be "similar" if every angle of one triangle has the same measure as the corresponding angle in the other triangle. The corresponding sides of similar triangles have lengths that are in the same proportion, and this property is also sufficient to establish similarity. Some basic theorems about similar triangles are: Two triangles that are congruent have exactly the same size and shape: all pairs of corresponding interior angles