Chapter 12.2, Problem 4C

To determine

To generalize : The sentence from two-dimensional to three-dimensional.

Answer to Problem 4C

From any point inside a triangular pyramid whose edges have same length, the sum of projections on to the faces of the pyramid equals to the height of pyramid.

Explanation of Solution

Let suppose a point inside an equilateral triangle.

  

From theorem, it is known that

  $x+y+z=h$

From any point inside an equilateral triangle, the sum of perpendiculars on the sides is equal to the altitude of the triangle.

Now, generalize the above statement to three-dimensional:

“From any point inside a triangular pyramid whose edges have same length, the sum of projections on to the faces of the pyramid equals to the height of pyramid”.