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问题: 如图,在菱形ABCD中,点E在BC边上,且AB=AE,∠BAE=1/2∠EAD,AE交BD于点M,试

如图,在菱形ABCD中,点E在BC边上,且AB=AE,∠BAE=1/2∠EAD,AE交BD于点M,试说明BE=AM

解答:

解:∵AB=AE ∴∠ABE=∠AEB=∠EAD
∵∠BAE=1/2∠EAD ∴∠EAD=2∠BAE ∴5∠BAE=180°
∠BAE=36°∠ABE=∠AEB=∠EAD=72°
∵菱形ABCD ∴∠ABD=∠DBC=72°/2=36°=∠BAE
即:∠ABD=∠BAE AM =BM