Download Fun geometry 7.1 note sheet Chapter 7 packet Find the geometric

Fun geometry
Chapter 7 packet
7.1 note sheet
Find the geometric mean between the two numbers:
1) 8 and 6
2) 4 and 9
3) 2 2 and 6 2
1
1)
2)
3)
4)
Find x and/or y:
5)
6)
x
y
x
x = ______
x = ________, y = ________
2
Leave answers in exact form, reduced.
√6 and √6
Solve for each variable. Express answers in exact form.
15)
ans
wer
s in
exa
ct
for
m,
red
18)
uce
ans
d.wer
s in
exa
ct
for
m,
red
uce
d.
16)
ans
wer
s in
exa
ct
for
m,
red19)
uce
ans
d. wer
s in
exa
ct
for
m,
red
uce
d.
17)
ans
wer
s in
exa
ct
for
m,
red
20)
uce
ans
d.
wer
s in
exa
ct
for
m,
red
uce
d.
3
4
Geometry Notes Section 7.2:
The Pythagorean Theorem and Its Converse
The Pythagorean Theorem: In a right triangle, the sum of the squares of the __________ is equal to
the ______________________________.
Acute triangle: __________________________
Right triangle: __________________________
Obtuse triangle: _________________________
Pythagorean Triple: Three _________ numbers that can form sides of a right triangle.
______________, _______________, and ______________.
Examples:
1)
2)
3)
Determine if the following vertices form a right, obtuse, or acute triangle. Show all work and explain.
4) 11, 4, 10
5) 5, 6, 4
6) W(-3, 6) T(5, 5)
Y(3, 2)
5
The Pythagorean Theorem
Give all answers in exact form unless noted differently.
1)
The sides of a rectangle are 7 inches long and 9 inches long.
Find the length of the diagonal.
2)
The diagonal in a square is 16 cm long. Find the length of the sides.
3)
The base of an isosceles triangle is 8 ft long and the height is 3 ft.
Find the length of the legs.
4)
The perimeter of an equilateral triangle is 30 inches. Find the length of the altitude.
5)
If a man travels east 3 miles and south 2.5 miles, approximately how far is he
from his starting point?
6)
A triangle has sides of 14, 18 and 15. Classify the triangle as acute, obtuse or right.
6
10)
ans
wer
s in
exa
ct
for
13)
m,
ans
red
wer
uce
s in
d.
exa
ct
for
11)
ans
wer
s in
exa
ct
for
14)
m,
ans
red
wer
uce
d.s in
exa
ct
12)
ans
wer
s in
exa
ct
for
m,15)
redans
ucewer
d. s in
exa
ct
7
7.1-7.2 practice
12.
ans
wer
s in
exa
13.
ans
wer
s in
exa
14.
ans
wer
s in
exa
15.
ans
wer
s in
exa
8
Do the following sides form an acute, right or obtuse triangle? Show work.
Leave answers in exact form.
12
Decide if the following vertices form an acute, right or obtuse triangle.
9
Decide if the following vertices form an acute, right or obtuse triangle.
Decide if the following sides of a triangle form an acute, right or obtuse triangle.
Identify any Pythagorean triples.
10
45-45-90 Triangles
Problems 1 to 3. Write the decimal value (rounded to the nearest tenth)
3 2 =
1)
2)
2 5 =
3)
5 2 =
Problems 4 to 6. Solve for x and express it in simplest radical form.
4)
5)
6)
x
3
4
x
x
Problems 7 to 18. Solve for x and express it in simplest radical form.
7)
8)
9)
17
x
x
45
x
10)
11)
12)
x
x
x
45
13)
14)
15)
x
12
x
45
x
200
16)
17)
18)
x
2
x
x
Problems 19 to 21. Simplify each radical.
19)
22)
4 2 
20)
 81 
23)
2
2
24
21)
2  5 14 =
24)
5  80 =
3
7
5
11
Problems 25 to 42. Solve for x and express it in simplest radical form.
25)
26)
27)
9
x
x
x
28)
29)
30)
x
x
45
x
31)
32)
32
33)
x
x
45
x
34)
35)
36)
x
30
38
x
45
x
37)
38)
39)
x
x
x
40)
41)
42)
x
x
23 2
x
12
45-45-90 special right triangles
Name: ____________________________________
13
14
30-60-90 Triangles
Rewrite each expression into simplest radical form.
1)
75
2)
3)
3 7 
2
4)
 18 
2
20  10
Find x and y. Put the answer in simplest radical form.
5) x = _______, y = __________
6) x = _______, y = __________
x
4
13
30
x
60
y
y
7) x = _______, y = __________
8) x = _______, y = __________
x
60
y
2
30
10
9) x = _______, y = __________
x
11) x = _______, y = __________
10) x = _______, y = __________
30
y
12) x = _______, y = __________
18
30
y
y
x
30
y
x
x
30
y
x
15
Find x and y. Put the answer in simplest radical form.
13) x = _______, y = __________
x
14) x = _______, y = __________
x
60
30
y
y
15) x = _______, y = __________
16) x = _______, y = __________
x
60
x
y
30
17) x = _______, y = __________
y
18) x = _______, y = __________
12
30
x
y
x
30
y
19) x = _______, y = __________
20) x = _______, y = __________
5
x
30
x
y
30
y
21) x = _______
1
22) x = _______, y = __________
5
45
x
y
x
16
30-60-90 special right triangles
17
18
10)
11)
13)
14)
12)
15)
16) A square had a diagonal of 2√6 𝑖𝑛 find the perimeter.
17) An equilateral triangle has a perimeter of 30m, find the altitude.
19
20
21
Answer the following in exact form
13.
14.
15.
22
11.
12.
13.
14.
15.
16.
17.
23
7)
8)
9)
10)
11)
12)
13)
14)
24
7.4 Trigonometric ratios
For any acute angle in a right triangle the following ratios are formed:
Sine
sin(angle) = _________________
Cosine
cos (angle) = ________________
Tangent
tan(angle) = _________________
Give the side adjacent <A
______________________
B
Give the side opposite <A
c
______________________
A
Give the hypotenuse:
______________________
Give the side opposite <B
______________________
Give the side adjacent <B
______________________
a
b
C
B
12
Give the following ratios rounded 4 decimal places
A
11
C
(hint: first find BC)
1) Sin<A = _________
2) tan<A = _________
3) Sin<B = _________
4) cos<A = _________
5) Tan<B = _________
6) cos<B = _________
25
Solving for right triangles using trigonometry
Round all angles to the nearest degree and all ratios to the nearest ten thousandth.
1) tan Z = 0.1944
14
5
3) cos Q 
m<Z = __________ 2) Cos (10) = x
x = __________
m<Q = __________ 4) Sin(40) = x
x = __________
Round all side measures to the nearest tenth and all anges to the nearest degree
5)
6)
x
x = __________
25
x = __________
x
20
7)
8
5
x 75
32
8)
10.8
9)
10)
5
3
x
x = __________
38
x = __________
51
x = __________
6
x = __________
x
x
11)
12)
400
x 81
x
25
x = __________
20
x = __________
13)
x
14)
24
6
x
4
26
27
28
29
30
9.
10.
11.
12.
14.
13.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
31
30.
31.
32.
7.5 word problems
1)
2)
3)
4)
5)
6)
7)
8)
32
7.5 book problems
1.
2.
3.
4.
**1 kilometer = 1000 meters
33
5.
6.
7.
8.
34