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解：$\because$四边形$ABCD$是正方形，

$\therefore AB = AD$，$BC = DC$．在$\triangle ABC$和$\triangle ADC$中，$\begin{cases} AB = AD, \\BC = DC, \\AC = AC, \end{cases}$$\therefore \triangle ABC \cong \triangle ADC$．$\therefore \angle BAC = \angle DAC = 45°$．

解：$\because$四边形$ABCD$是正方形，

$\therefore AB = AD$，$BC = DC$．在$\triangle ABC$和$\triangle ADC$中，$\begin{cases} AB = AD, \\BC = DC, \\AC = AC, \end{cases}$$\therefore \triangle ABC \cong \triangle ADC$．$\therefore \angle BAC = \angle DAC = 45°$．

解：$\because AC = BD$，
$\therefore AC + CD = BD + CD$，即$AD = BC$．
在$\triangle PAD$和$\triangle PBC$中，
$\begin{cases} PA = PB, \\AD = BC, \\PD = PC, \end{cases}$
$\therefore \triangle PAD \cong \triangle PBC$．
解：$\because AC = BD$，
$\therefore AC + CD = BD + CD$，即$AD = BC$．
在$\triangle PAD$和$\triangle PBC$中，
$\begin{cases} PA = PB, \\AD = BC, \\PD = PC, \end{cases}$
$\therefore \triangle PAD \cong \triangle PBC$．
有，还可以通过$\triangle ADE$和$\triangle CDE$全等来证明$AD = CD$．
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