如图平行四边形ABCD中,AC=根号2AB,求证:∠ABD=∠DAC
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/30 05:34:07
![如图平行四边形ABCD中,AC=根号2AB,求证:∠ABD=∠DAC](/uploads/image/z/3567579-51-9.jpg?t=%E5%A6%82%E5%9B%BE%E5%B9%B3%E8%A1%8C%E5%9B%9B%E8%BE%B9%E5%BD%A2ABCD%E4%B8%AD%2CAC%3D%E6%A0%B9%E5%8F%B72AB%2C%E6%B1%82%E8%AF%81%EF%BC%9A%E2%88%A0ABD%3D%E2%88%A0DAC)
xP1
@(XJػ
D;ӨڨH"&!1!\&1V;Ύfr7V(=[ҲTe{Փ'&Zr0
Xa:T4LCu
6g<[D\4
Dc9N{`9k'mW2swA
,ȇ-l#qǦ%,bDa/TYˆz |
如图平行四边形ABCD中,AC=根号2AB,求证:∠ABD=∠DAC
如图平行四边形ABCD中,AC=根号2AB,求证:∠ABD=∠DAC
如图平行四边形ABCD中,AC=根号2AB,求证:∠ABD=∠DAC
设AC与BD相交于O
∵AC=根号2AB,AO=OC(平行四边形的性质)
∴AC=2AO
∴AB=根号2AO
∴AB:AO=AC:AB=根号2
又∵∠BAC=∠OAB
∴△BAC∽△OAB
∴∠ABD=∠ACB
∵ABCD为平行四边形
∴∠DAC=∠ACB
∴∠ABD=∠DAC
.