Một số hệ thức về cạnh và đường cao trong tam giác vuông

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Bài 16: Cho tam giác ABC vuông tại A, có đường cao AH.

Giải bài toán trong các trường hợp sau:

a) Cho AC = 4 cm, BC = 5 cm. Tính AB, AH, BH, CH.

b) Cho AB = 12 cm, BH = 6 cm. Tính AH, AC, BC, CH.


Bài 17: Cho tam giác ABC vuông tại A. Đường phân giác AD chia cạnh đối diện BC thành hai đoạn BD = 36cm, DC = 60cm. Hạ đường cao AH. Tính tỉ số HB:HC  và tính AH?

Bài 18: Cho tam giác ABC vuông tại A. Biết rằng , đường cao AH = 30cm. Tính HB, HC


Bài 19: Cho tam giác ABC vuông tại A , đường cao AH, AB =20cm, HC = 9cm. Tính AH.


Bài 20: Cho ▲ABC có AB = 6 cm ; BC = 10cm, AC = 8cm. Tính đường cao AH.


Bài 21:  Cho ▲ABC có BH là đường cao,AB = 6 cm, BC = 8cm, AC = 10cm.

a ) Chứng tỏ: ▲ABC vuông tại B ? 

b )  Từ H kẻ HE ^ AB ; HF ^ BC . Chứng minh BEHF là HCN.

c ) Chứng minh :  BE .BA= BF . BC    

d )  Tính diện tích ▲HEF  ?


Bài 22: Cho hình chữ nhật ABCD có AB = 2 BC. Trên cạnh BC lấy điểm E. Tia AE cắt CD tại F. Chứng minh rằng: 


Bài 23: Tam giác ABO vuông tại O. Gọi C là hình chiếu của O trên AB, D và E là hình chiếu của C trên OA và OB. Chứng minh rằng:

a) 


b) OC3=AB.DA.ED

c) AB2 = 3.OC2 + AD2 + EB2

Bài 24: Cho hình chữ nhật ABCD. Vẽ DE^AC tại E. Gọi M, N, I là lượt là trung điểm của BC, AE, DE. Chứng minh rằng:

a) AE:CE =(BC:AB)2

b) I là trực tâm của tam giác CDN

c) MN2+ND2=CM2 + CD2


Bài 25 :Cho hình chữ nhật ABCD biết AB = 8 cm, AD = 6cm 

a)  Kẻ đường cao AH của tam giác ABD. Tính khoảng cách từ điểm H đến các đỉnh của tam giác ABD.


b) Đường thẳng AH cắt CD tại E. Chứng minh: 


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