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D
?$?? 解：四邊形ABCD是矩形??$?
?$?? ∵BC為等腰△BED的底邊上的高\(yùn) $?
?$∴EC=CD??$?
?$?? ∵四邊形ABEC是平行四邊形 ??$?
?$?? ∴AB//CD，AB=CD=CE,AC=BE$?
?$∴四邊形ABCD是平行四邊形??$?
?$?? ∵AC=BE,BE=BD$?
?$∴AC=BD?$?
?$?∴四邊形ABCD是矩形.??$?
$?證明：??? ∵A B，?????? A D ???分別為角平分線$
$??? ∴\angle B A C+\angle D A C=90° ，??? 即??? \angle B A D=90° ???$
$同理??? \angle B C D=90° ???$
$??? ∵M(jìn) N / / P Q???$
$??? ∴\angle M A C+\angle A C P=180° ???$
$??? ∴\angle B C A+\angle B A C=90° ，??? 即??? \angle A B C=90° ???$
$∴四邊形???ABCD???是矩形$
B
7
?$證明：???(1)∵∠BAD=∠CAE ???$?
?$ 在???△ABE???和???△ACD???中$?
?$??? \begin{cases}AE=AD\\∠EAB=∠DAC\\AB=AC\end{cases}???$?
?$??? ∴△ABE≌△ACD(\mathrm {SAS})???$?
?$??? (2)???四邊形???BCDE???是矩形$?
?$??? ∵△ABE≌△ACD ???$?
?$??? ∵DE=BC ???$?
?$??? ∵AE=AD ???$?
?$??? ∴∠AEB-∠AED=∠ADC-∠ADE，???即???∠DEB=∠EDC???$?
?$??? ∵∠BED+∠EDC=180°???$?
?$??? ∴∠DEB=∠EDC=90°???$?
?$ ∴四邊形???BCDE???是矩形$?
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