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Kite. A kite is made up of two isosceles triangles joined base to base.
Lesson 7 Summary A parallelogram can always be decomposed into two identical triangles by a segment that connects opposite vertices.
Only a rhombus can be divided into two equilateral triangles, and a rhombus is a parallelogram. A rhombus with two 60 degree angles and two 120 degree angles can be split by one of its diagonals (the one that bisects the 120 degree angles) into two congruent, equilateral triangles.
Again, rigid motions (a rotation) show that the two polygonal arrangements are congruent. Hence, the total number of unique arrangements of 4 isosceles right triangles is 14!
There are two layouts of four equilateral triangles that will fold to make a tetrahedron and one that will not. Get students to identify why (two of the triangles fold to be on top of each other, so there is an open side).
Three triangles interlocked together form the valknut, an Old Norse word which roughly translates to the “knot of slain warriors.” The term, however, is modern, as archaeologists don’t really know what ancient Germanic tribes called this symbol or why they were etched or marked on artifacts.
The tangram is a set of seven geometric shapes made up of five triangles, a square, and a parallelogram.
When pointing up, they represent stability and power, when pointing down they become unstable. The triangle is primarily a masculine shape, but when inverted it also represents female reproduction. In spirituality, triangles represent the union of body, mind, and spirit.