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Faces of the tetrahedron are congruent triangle

Source:

October 15, 2010
geometry3D geometrytetrahedrongeometry proposed

Problem Statement

In a tetrahedron we know that sum of angles of all vertices is 180∘.180^\circ. (e.g. for vertex AA, we have ∠BAC+∠CAD+∠DAB=180∘.\angle BAC + \angle CAD + \angle DAB=180^\circ.) Prove that faces of this tetrahedron are four congruent triangles.
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