Bài tập chương I hình 9

BÀI TẬP HÌNH HỌC
1. Cho tam giác ABC vuông tại A; đường cao AH; AC=16cm, HB=7,2cm. Tính: AH, AC, BC, BH.
Vẽ hình:







Bài làm:
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2. Cho tam giác ABC vuông tại A; đường cao AH, đường trung tuyến AM.
a) Chứng minh: sin AMB = 2sin C cos C.
b) Chứng minh: 1 + cos AMB = 2 cos2 C.
c) Chứng minh: 1 – cos AMB = 2 sin2 C.
Vẽ hình:







Bài làm:
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3. Cho tam giác ABC có BC=20cm, góc B=45o, góc C=30o.
a) Tính S
?
b) Vẽ đường cao CF của
. Tính S
?
Vẽ hình:







Bài làm:
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4. Cho tam giác ABC vuông tại A, đường phân giác AD, đường cao AH. Biết BD=7,5cm và DC=10cm. Tính AH, BH, HD.
Vẽ hình:







Bài làm:
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5. Cho tam giác ABC có BC=20cm, góc B= 50o, góc C=70o.
a) Vẽ CH
AB. Tính CH, AC?
b) Chứng minh: S
=
.
c) Chứng minh:

Vẽ hình:







Bài làm:
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5. Cho tam giác ABC vuông tại A; đường cao AH; biết AB=5cm, AC=12cm; vẽ HE
AB tại E và HF
AC tại F.
a) Tính BH, AH, CH?
b) Chứng minh AB.AE=AC.AF
c) Vẽ AM là phân giác góc BAC. Tính AM?
Vẽ AD là phân giác góc HAC. Tính AD?
d) Chứng minh: BC2=3AH2+BE2+CF2
e) Tính S
?
f) Chứng minh:

g) Chứng minh: AH3=BC.BE.CF=BC.HE.HF
h) Chứng minh:

i) Chứng minh:

k) Chứng minh:

l) Chứng minh: BC=AB.cos B+AC.cos C
Chứng minh: BC=AB.sin C+AC.sinB
m) Chứng minh: AH2=AB.AC.cos B.cos C
n) Cho sinB=sin7C+sin6BsinC+3sin3Csin2B.Tính
?
Vẽ hình:







Bài làm:
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