GRE Sample Test 4 Quantitative Reasoning 1

Right triangles ABD and CDB share a hypotenuse, segment DB. The shared hypotenuse should clue you to use the Pythagorean theorem. See that w and x are lengths of the legs of right triangle ABD; side AD has length w, side AB has length x. Also, y and z are lengths of the legs of right triangle CDB; side CD has length z, side CB has length y. Where a and b are lengths of the legs of a right triangle, and c is the length of the hypotenuse, ${\mathit{a}}^2+{\mathit{b}}^2$ = ${\mathit{c}}^2$. So here ${\mathit{w}}^2+{\mathit{x}}^2$ = length $\mathit{B}{\mathit{D}}^2$; ${\mathit{y}}^2+{\mathit{z}}^2$ also equals length $\mathit{B}{\mathit{D}}^2$. The quantities are equal, and the answer is (C).