EncleVes2020

5 tháng trước

Cho hình bình hành `ABCD` cps đường chéo `AC` lớn hơn đường chéo `BD` . Gọi E;F lần lượt là hình chiếu của `B` và `D` trên đường thẳng `AC`. Gọi `H` và `K` lần lượt là hình chiếu của `C` trên đg thẳng `AB` và `AD` `a)` Tứ giác `BDEF` là hình gì tại sao `b)` Chứng minh `CH.CD=CB.CK` `\text{NHỚ VẼ HÌNH}`

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Oriana008

5 tháng trước

`a)` Ta có : `BE⊥AC` ( gt)

`DF⊥AC` ( gt)

`=>BE` $// DF$

`\Delta BEO= \Delta DFO` ( g.c.g ) `=>BE=DF`

`=>` Tứ giác `BDEF` là hình bình hành

`b)` Ta có : `\hat{ABC}=\hat{ADC}=>\hat{HBC}=\hat{KDC}`

`=>\Delta CBH` $\backsim$ `\Delta CDK` (g.g)

`=>(CH)/(CB)=(CK)/(CD)`

`=>CH.CD=CB.CK` ( đpcm)

nhung0

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