Viviani's theorem states that the sum of altitudes to all sides from a point inside one of these is 
Viviani's theorem states that the sum of altitudes to all sides from a point inside one of these is equal to the length of its altitude. Morley's theorem states that one of these is formed by extending the trisectors of a triangle. Napoleon's theorem states that a fourth one of these can be produced by joining the centroids of ones erected on the sides of any triangle, and they are the repeating units of a Koch snowflake and Sierpinski's triangle. For 10 points, identify these geometric figures which have three congruent sides.
Viviani's theorem states that the sum of altitudes to all sides from a point inside one of these is equal to the length of its altitude.
{equilateral} triangles [prompt on {equiangular} triangles; prompt on triangles]