MathDB

5

Part of 1997 Taiwan National Olympiad

Problems(1)

tetrahedron

Source: 6-th Taiwanese Mathematical Olympiad 1997

1/18/2007
Let ABCDABCD is a tetrahedron. Show that a)If AB=CD,AC=DB,AD=BCAB=CD,AC=DB,AD=BC then triangles ABC,ABD,ACD,BCDABC,ABD,ACD,BCD are acute. b)If the triangles ABC,ABD,ACD,BCDABC,ABD,ACD,BCD have the same area , then AB=CD,AC=DB,AD=BCAB=CD,AC=DB,AD=BC.
geometry3D geometrytetrahedrontrigonometryparallelogramgeometry proposed