A Rectangle Identity, Generalized

★ 6/10plane geometry solid geometry Symmetry

Problem

1. Let $P$ be any point in the plane of rectangle $ABCD$ . Prove that

PA^2 + PC^2 = PB^2 + PD^2.

Generalize to a point $P$ anywhere in space, and prove your statement.
Generalize further to a rectangular box $ABCD\text{–}A_1B_1C_1D_1$ : formulate and prove an analogous identity using part 2.

Answer

Solution

Difficulty	6/10
Topics	plane geometry, solid geometry, Symmetry

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