Question

[Ha Thi Dinh Trung tam thuc hanh may]

Cho \(\Delta ABC\) vuông tại A, đường cao AH.

a)  CM:  \(\Delta ABC\)đồng dạng \(\Delta HBA\)

b)   Tính BH?  biết AB=3cm,  AC=4m

c)  Kẻ HK vuông góc với AC. CM:   \(\Delta AHC\)và \(\Delta AKH\)đồng dạng, từ đó => \(AH^2=AK.AC\)

d)   Kẻ HI vuông góc với AB, Các tia HI, HK cắt 1 đường thẳng a bất kì qua A lần lượt tại E, F. Chứng minh \(\frac{CK}{FI}=\frac{KE}{IA}\)

Answer 1

[Nguyễn Quỳnh Trang]

ttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt

Answer 2

[Nguyễn Linh Chi]

a) 

Xét \(\Delta\)ABC và \(\Delta\)HBA có: 

^BAC = ^BHA ( = 90 độ ) 

^ABC = ^HBA ( ^B chung ) 

=> \(\Delta\)ABC ~ \(\Delta\)HBA 

b) AB = 3cm ; AC = 4cm 

Theo định lí pitago ta tính được BC = 5 cm 

Từ (a) => \(\frac{AB}{BH}=\frac{BC}{AB}\Rightarrow BH=\frac{AB^2}{BC}=1,8\)m 

c) Xét \(\Delta\)AHC và \(\Delta\)AKH có: ^AKH = ^AHC = 90 độ 

và ^HAC = ^HAK ( ^A chung ) 

=> \(\Delta\)AHC ~ \(\Delta\)AKH 

=> \(\frac{AH}{AK}=\frac{AC}{AH}\Rightarrow AH^2=AC.AK\)

d) Bạn kiểm tra lại đề nhé!