At the base of the pyramid is a square, the height of the pyramid is equal to the side of the square

| February 20, 2021 | education

At the base of the pyramid is a square, the height of the pyramid is equal to the side of the square and passes through one of the vertices, define the dihedral angles at the base of the pyramid.

Since the edge of the KС is perpendicular to the base, the triangles KСD and KСВ are rectangular.

By condition, AB = BC =СD = AD = KС, then the КСВ and KСD triangles are rectangular and isosceles, and therefore their acute angles are 45.

The projections of the lateral edges KD and KB on the plane of the base of the pyramid are the sides of the base of the СD and ВС, which are perpendicular to AD and AB, then the inclined KD and KB are also perpendicular, and the triangles ADС and ABС are then dihedral angles between the base of the pyramid and the lateral faces of KСD and KСВ these are the angles of KDС and KВС and are equal to 45.

Answer: The dihedral angles at the base are 45.



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