ÔN CHƯƠNG I – HÌNH HỌC 9
PHIẾU BÀI TẬP
Thời gian giao: Thời gian hoàn thành:
Nội dung: Ôn tập chương I
Hệ thức lượng trong tam giác vuông
Name: Lớp: 9….
Phần 1. HỆ THỨC GIỮA CẠNH VÀ ĐƯỜNG CAO
STT Công thức Đối tượng trong hệ thức Nội dung ngắn gọn
1
b
2
= a.b’
c
2
= a.c’
Cạnh góc vuông
Hình chiếu
Cạnh huyền
(Cạnh góc vuông)
2
= Cạnh huyền . hình chiếu
2 h
2
= b’.c’
Đường cao
2 hình chiếu
(Đường cao)
2
= hình chiếu 1 . hình chiếu 2
3 b.c = a.h
2 cạnh góc vuông

Cạnh huyền
Đường cao
Cạnh gv 1 . Cạnh gv 2 = cạnh huyền . đường cao
4
2 2 2
1 1 1
h b c
= +
Đường cao
2 cạnh góc vuông
( ) ( ) ( )
2 2 2
1 1 1

= +
5
Pitago
a
2
= b
2
+ c
2
Cạnh huyền
2 cạnh góc vuông
(Cạnh huyền)
2
= (Cạnh GV1)
2
+ (Cạnh GV2)

2
Bài tập vận dụng 1: Cho tam giác ABC vuông ở A có đường cao AH. Trong các đoạn thẳng AB, AC,
BC, AH, BH, CH hãy tính độ dài các đoạn thẳng còn lại nếu biết.
a) AB = 6cm; AC = 8cm. Tính ........................................................
..................................................................................................................................................
..................................................................................................................................................
..................................................................................................................................................
..................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
b) AB = 15cm; HB = 9cm. Tính ………………………………………
..................................................................................................................................................
..................................................................................................................................................
..................................................................................................................................................
..................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
VietNam Australia International School Trang 1
ÔN CHƯƠNG I – HÌNH HỌC 9
c) AC = 44cm; BC = 55cm. Tính …………………………………………
..................................................................................................................................................
..................................................................................................................................................
..................................................................................................................................................
..................................................................................................................................................

................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
d) AC = 40cm; AH = 24cm. Tính ………………………………………….
..................................................................................................................................................
..................................................................................................................................................
..................................................................................................................................................
..................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
e) AH = 9,6cm; HC = 72cm. Tính …………………………………………………………………….
..................................................................................................................................................
..................................................................................................................................................
..................................................................................................................................................
..................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................

................................................................................................................................................................................................................................................
VietNam Australia International School Trang 2
ÔN CHƯƠNG I – HÌNH HỌC 9
Bài tập áp dụng 2. Cho tam giác ABC vuông tại A có đường cao AH, phân giác AD. Biết BD = 15cm,
DC = 20cm. Tính AH, AD ?
..................................................................................................................................................
..................................................................................................................................................
..................................................................................................................................................
..................................................................................................................................................
..................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
Bài tập áp dụng 3. Cho tam giác ABC cân ở A có đường cao AH = 32cm, đường cao BK = 38,4cm.
a) Tính các cạnh của tam giác ABC.
b) Đường trung trực của AC cắt AH tại O. Tính OH?
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................

................................................................................................................................................................................................................................................
VietNam Australia International School Trang 3
ÔN CHƯƠNG I – HÌNH HỌC 9
Phần 2. TỈ SỐ LƯỢNG GIÁC CỦA GÓC NHỌN
* Một số tính chất khác:
- Nếu hai góc phụ nhau thì sin góc này bằng cosin góc kia, tang góc này bằng cotang góc kia.
- Với góc nhọn
α
bất kỳ ta luôn có:
0 < sin
α
< 1 ; 0 < cos
α
< 1
2 2
sin cos 1
α α
+ =

sin cos
; co ; .co 1
cos sin
tg tg tg tg
α α
α α α α
α α
= = =
Bài tập áp dụng 1. Cho góc nhọn
α
, biết sin

α
= 0,6. Hãy tính các tỉ số lượng giác còn lại của
α
.
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
Bài tập áp dụng 2. Cho tam giác ABC vuông tại A, biết sinB = 0,4. Hãy tính các tỉ số lượng giác của góc
A.
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
VietNam Australia International School Trang 4
Sin B = ------ Sin C = -------
Cos B = ------ Cos C = -------
Tg B = ------ Tg C = -------
Cotg B = ------ Cotg C = -------
ÔN CHƯƠNG I – HÌNH HỌC 9

Bài tập áp dụng 3. Tính giá trị các biểu thức:
a) A = (sin1
o
+ sin2
o
+ sin3
o
+ …. + sin88
o
+ sin89
o
) – (cos1
o
+ cos2
o
+ cos3
o
+ ….+ cos88
o
+ cos89
o
)
b) B = tg1
o
. tg2
o
. tg3
o
…..tg88
o

.tg89
o
c) C = cotg1
o
. cotg2
o
. cotg3
o
….. cotg88
o
. cotg89
o
d) D = sin
2
1
o
+ sin
2
2
o
+ sin
2
3
o
+ …. + sin
2
88
o
+ sin
2

89
o
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
Bài tập áp dụng 4. Chứng minh rằng với góc nhọn
α
bất kỳ ta có:
a)
2 2
2 2
1 1
1 ; 1+co
cos sin

tg tg
α α
α α
+ = =
b)
4 4 2 2
sin cos 1 2sin .cos
α α α α
+ = −
c)
4 4 2
sin cos 1 2cos
α α α
− = −
d)
2 2 2 2
sin .sintg tg
α α α α
− =
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
................................................................................................................................................................................................................................................
VietNam Australia International School Trang 5