twotriangle

Twotriangle is a term used in geometry to denote a simple polygon formed by joining two triangles along a common side. The resulting figure is a quadrilateral, with the shared side forming an interior edge that is common to both component triangles.

Construction: Given two triangles that share a side, place them so their interiors lie on opposite sides of that edge; the union is the twotriangle. If the two triangles are congruent, the figure is a kite, having two pairs of adjacent equal sides and a line of symmetry perpendicular to the shared side. If the triangles are not congruent, the shape is a general quadrilateral with the two original triangles as a partition.

Properties: The area equals the sum of the areas of its component triangles. The boundary consists of four edges; the shared edge is not an exterior edge of the quadrilateral. The angles at the endpoints of the shared edge are the sums of the corresponding angles from each triangle.

Applications: Used in basic geometry instruction to demonstrate area addition, polygon composition, and congruence. It also arises in tiling and polyform contexts where two-triangle units combine to create larger shapes. In computer graphics, twotriangle models can simplify rendering of adjacent triangular facets.

See also: triangle, quadrilateral, kite, rhombus, tiling, polyiamond.