6. Let $P$ be any point on the hypotenuse $AC$ of an isosceles right $\triangle ABC$, $PE \perp AB$ at $E$, $PF \perp BC$ at $F$, $PG \perp EF$ at $G$, and take a point $D$ on the extension of $GP$ such that $PD = PB$. Then the relationship between $BC$ and $DC$ is ( ).
(A) equal but not perpendicular
(B) not equal but perpendicular
(C) equal and perpendicular
(D) not equal and not perpendicular
6. $\mathrm{C}$ (Hint: Prove $\triangle D P C \cong \triangle B P C$ )



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