Question

 

Cho tam giác nhọn ABC có hai đường cao BD và CE cắt nhau tại H.

Chứng minh rằng : BH.BD + CH.CE = BC².

ai làm đc mình tick cho

Answer 1

HF" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">HF vuông góc BC. Ta có:

△BFH∼△BDC" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">△BFH∼△BDC

⇒BFBD=BHBC⇒BF.BC=BD.BH" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">⇒BFBD=BHBC⇒BF.BC=BD.BH

△CFH∼△CEB" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">△CFH∼△CEB

⇒CFCE=CHCB⇒CF.BC=CE.CH" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">⇒CFCE=CHCB⇒CF.BC=CE.CH

BC2=BF.BC+CF.BC=BD.BH=CE.CH" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">BC2=BF.BC+CF.BC=BD.BH=CE.CH" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">Mk copy tai nguon :http://diendantoanhoc.net/topic/95087-ch%E1%BB%A9ng-minh-r%E1%BA%B1ng-bc2bhbdchce/

Answer 2

Minh khong chac dung cho lam dau nhe : 

BD+DC=2BC(BC la canh huyen cua tam giac BDC)

EC+BE=2BC(BC la canh huyen cua tam giac BEC)

=>BH.BD+CH.CE=BC²

Answer 3

to cung ra vay