（本题满分10分）（1）如图①，在正方形ABCD中，△AEF的顶点E，F分别在...

（本题满分10分）

（1）如图①，在正方形ABCD中，△AEF的顶点E，F分别在BC，CD边上，高AG与正方形的边长相等，求的度数．

（2）如图②，在Rt△ABD中，，，点M，N是BD边上的任意两点，且，将△ABM绕点A逆时针旋转至△ADH位置，连接，试判断MN，ND，DH之间的数量关系，并说明理由．

（3）在图①中，连接BD分别交AE，AF于点M，N，若，，，求AG，MN的长．

说明: 6ec8aac122bd4f6e

（1）在Rt△ABE和Rt△AGE中，，， ∴△ABE≌△AGE． ∴．················································· 1分同理，． ∴．······································································ 2分（2）．······································································ 3分 ∵，， ∴． ∴．又∵，， ∴△AMN≌△AHN． ∴．························································· 5分 ∵，， ∴． ∴． ∴． ∴．···································· 6分（3）由（1）知，，．设，则，． ∵， ∴．解这个方程，得，（舍去负根）． ∴．························································································· 8分 ∴．在（2）中，，， ∴．·········································································· 9分设，则． ∴．即．···································································· 10分【解析】略

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