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plane forms equal angles with 2 planes, pyramid with base rectangle

Source: 2012 Romania District VIII P2

May 19, 2020
geometry3D geometrypyramidanglesplanes

Problem Statement

The pyramid VABCDVABCD has base the rectangle ABCD, and the side edges are congruent. Prove that the plane (VCD)(VCD) forms congruent angles with the planes (VAC)(VAC) and (BAC)(BAC) if and only if ∠VAC=∠BAC\angle VAC = \angle BAC .
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