Equal areas in a pyramid
Source: 2023 Israel TST Test 1 P2
March 23, 2023
TSTgeometryareas3D geometrypyramid
Problem Statement
Let be a pyramid whose base is a regular pentagon and whose other faces are acute triangles. The altitudes from to the base sides dissect them into ten triangles, colored red and blue alternatingly. Prove that the sum of the squared areas of the red triangles is equal to the sum of the squared areas of the blue triangles.