已知,如图AB=AC,AD=AE,∠ BAC=∠ DAE=90° ,M是BE中点,求证：AM⊥DC

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已知,如图AB=AC,AD=AE,∠BAC=∠DAE=90°,M是BE中点,求证：AM⊥DC已知,如图AB=AC,AD=AE,∠BAC=∠DAE=90°,M是BE中点,求证：AM⊥DC已知,如图AB=

已知,如图AB=AC,AD=AE,∠ BAC=∠ DAE=90° ,M是BE中点,求证：AM⊥DC
已知,如图AB=AC,AD=AE,∠ BAC=∠ DAE=90° ,M是BE中点,求证：AM⊥DC

已知,如图AB=AC,AD=AE,∠ BAC=∠ DAE=90° ,M是BE中点,求证：AM⊥DC
AM于CD的交点为点N,延长AM到F,使MF=AM
∵BM=EM
∴ABFE是平行四边形
∴BF=AE ∠ABF+∠BAE=180°
∵∠BAC=∠DAE=90°
∴∠CAD+∠BAE=180°
∴∠ABF=∠CAD
∵BF=AE AD=AE
∴BF=AD
∵AB=AC
∴△ABF ∽△CAD
∴∠BAF=∠ACD
∵∠BAC=90°
∴∠BAF+∠CAN=90°
∴∠ACD+∠CAN=90°
∴∠ANC=90°
∴AM⊥CD

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