解几道数学证明题

2024-12-29 17:14:19
推荐回答(2个)
回答1:

是的!

水平线BD⊥甲楼AC
夹角相等∠ABD=∠CBD
BD=BD
Rt△ABD≌Rt△CBD
AD=CD
AC=2AD
AD=乙楼高
甲楼=2*乙楼的高。

选为满意回答

2、在△ADC和△BDC中
∠ADC=∠BDC
CD=CD

∠ACD=∠BCD

∴△ADC≌△BDC
∴AC=BC

又AC=100M

∴BC=100M

3、(1)解:∠CAF=∠DAG.
理由:∵Rt△ABC中,∠C=90°,将△ABC沿AB向下翻折后,再绕点A按顺时针方向旋转α度(α<∠BAC),得到Rt△ADE,
∴∠BAC=∠EAD,
∵∠BAC=∠CAF+∠BAE,∠EAD=∠DAG+∠BAE,
∴∠CAF=∠DAG;

(2)证明:∵将△ABC沿AB向下翻折后,再绕点A按顺时针方向旋转α度(α<∠BAC),得到Rt△ADE,
∴AC=AD,∠C=∠D=90°,
在△ACF和△ADG中,

∠C=∠D
AC=AD
∠CAF=∠DAG

∴△ACF≌△ADG(ASA).

选为满意回答

回答2:

答:甲楼的高度是乙楼的2倍。
设甲楼顶部为C,乙楼底部为D。过B点作BE垂直于AC,则易证四边形BEAD是矩形,所以
AE=BD。
又因为两盏灯的光线与水平线的夹角相等,则三角形ABC是等腰三角形,BE是顶角平分线,
由“三线合一”可得BE是底边上的中线,
所以AE=CE=BD,
所以AC=2BD即甲楼的高度是乙楼的2倍。

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