Download Geometry Final Exam Review – Ch. 7 Name

Geometry Final Exam Review – Ch. 7
SIMPLIFY each ratio completely.
40
18
1.
=
2.
=
24
33
Convert units to simplify each ratio.
4 days
3 ft .
6.
=
7.
=
2 weeks
8 inches
Name:_________________________________
Hour: ____
3.
20
=
35
4. 32 : 4 =
8.
6 yards
=
4 feet
9.
A basketball team won 12 games and lost 8. Reduce
each ratio.
40 cm
=
2 meter
5. 30 : 39 =
10.
8 cm
=
6 mm
15. In the diagram, JK : KL is 7 : 2 and JL =36.
Find JK and KL.
36
11. wins to losses
Equation:
12. wins to the total number of games played
13. losses to wins
14. losses to the total number of games played
x = _____ JK = _____ KL = ______
16. Use the triangles to write each ratio in simplest
form.
XY
 ________
RS
17. Use the triangles to write each ratio in simplest
form.
AX
XB
= _______
= _______
XB
AX
ST
 ________
YZ
AX
= _______
AB
BC
= _______
XY
XZ

RT
AY
= _______
YC
AY
= _______
AC
________
Solve these proportions by cross-multiplying. Use the distributive property where needed. Show your work!
2 x2
x  4 3x  2
x 6



18.
19. 8 : 3 = x : 6
20.
21.
9
8
5
10
5 4
Proportion:
Set up a PROPORTION to solve the following problems.
22. If 25 Valentine chocolate candies cost $20.00.
How much will 42 Valentine chocolates cost?
23. Thomas finished 50 math problems in 20 minutes.
At this rate, how many math problems can he do in 30
minutes?
Proportion:
Proportion:
Answer = __________
Answer = __________
24. Shapes that are SIMILAR are the same shape, but not necessarily the same _____________.
25. In SIMILAR shapes, the corresponding angles are _____________and the corresponding sides are
_____________________.
1
The two polygons are similar. Write a proportion and solve for x.
26.
27.
28.
Proportion to find x and solve:
Proportion to find x and solve:
Proportion to find x and solve:
29.
30.
31.
 LJK ~  _______ Scale Factor: _______
LMNP ~ _______ Scale Factor: ________
 DEF ~  _______ Scale Factor: _______
Proportion to find x:
Proportion to find x:
Proportion to find x: Proportion to find y:
Proportion to find y:
Proportion to find y:
32. The two rectangles are similar.
a. Find the scale factor (left to right).
33. The scale factor of two similar
triangles is 4 : 7, find the ratio of
the perimeters.
b. Find the ratio of the perimeters of the rectangles.
Determine if the triangles are similar by AA~, SSS~, SAS~, or none. Work must be shown to check proportions
and/or angles!
34.
35.
36.
Check Proportions and/or Angles:
Check Proportions and/or Angles:
Check Proportions and/or Angles:
Postulate: _________
Postulate: _________
Postulate: _________
37.
38.
39.
Check Proportions and/or Angles:
Check Proportions and/or Angles:
Check Proportions and/or Angles:
Postulate: _________
Postulate: _________
Postulate: _________
2
Find the missing angles and set up proportions to find the missing side lengths for the similar triangles.
40.
41.
Proportion to find x:
Proportion to find y:
Proportion to find x:
Proportion to find y:
mT= ______
mN = ______
mD = ______ mT = ______ mA = ______
42.
43.
"Flipped" or "Twisted" Bow Tie?
"Flipped" or "Twisted" Bow Tie?
 PET ~  _______
Proportion to find x:
CAB ~  _______
Proportion to find y:
Proportion to find x:
mP = ______ mATC = ______mA = ______
44.
Proportion to find y:
m1 = ______ mA = ______ mE = ______
45.
Separate and label triangles here:
Separate and label triangles here:
 EAB ~  _______ Scale Factor: ________
 BAC ~  _______Scale Factor: ________
Proportion to find x:
Proportion to find x:
Proportion to find y:
mE = ______ mD= ______ mF = ______
Proportion to find y:
mD = ______ mBCA = ______mA = ______
Complete the following proportions by using the picture at the right.
PQ
?
PQ PR


46.
? = _______ 47.
? = _______
PS PT
QS
?
QR
?
PQ QR
48.
? = _______ 49.
? = _______


ST PT
?
ST
3
Use a proportion to solve for the missing length.
49.
Proportion to find x:
50.
Proportion to find x:
51.
52.
Proportion to find z:
Proportion to find x:
Separate the picture into two labeled triangles and find the missing information.
53.
Separate the picture into two labeled triangles.
54.
Separate the picture into two labeled triangles
Proportion to find x:
Proportion to find y:
Proportion to find x:
Proportion to find y.
Use the MIDSEGMENT FORMULA to solve for the length of the variable.
55.
56.
57.
58.
x = ________
y = ________
a = ________
b = ________
4
Geometry Final Exam Review – Ch. 8
Name:_________________________________
Hour: ____
1. How do you find the perimeter of any shape?__________________________
Find the perimeter of each shape.
2.
3.
4.
5.
6-7. Draw a rectangle with the following dimensions.
6. Draw a rectangle with perimeter 12
and area 8.
7. Draw a rectangle with perimeter 10
and area 4.
Converting units. Fill in the blanks.
8. 1 yd = _____ feet
9. 2 yd = _____ feet
10. 6 feet = ____ yards
11. 12 feet = ____yards
12. 1 foot = ___ inches
13. 5 feet = ___inches
14. 24 inches = ___feet
15. 48 inches = ____ft
16. 1 meter = ____cm
17. 4 meters = ____cm
18. 5 cm = ____mm
19. 12 cm = ______mm
20. How do you find the area of a rectangle?_________________
21. How do you find the area of a parallelogram?_______________
Find the area of each rectangle or parallelogram.
22.
23.
24.
26.
27.
28.
25.
29.
Given the dimensions of a parallelogram, find the area.
30. base = 24 cm
31. base = 18 in
32. base = 16.2 m
height = 5 cm
height = 25 in
height = 9.4 m
5
33. base = 45 ft
height = 8 yd
Find x for each parallelogram.
34. Area = 48 cm2
35. Area = 63 in2
36. How do you find the area of a triangle?_____________________
Find the area of each triangle.
37.
38.
39.
40.
Find x for each triangle.
41. Area = 32 in2
42. Area = 24 in2
Fill in the following formulas.
43. Area of a trapezoid _____________________
44. Area of a rhombus __________________________
45. Area of a regular polygon ________________
Find the area of each shape.
46. A trapezoid with bases of length 10in and 12 in, and height 7 in.
47. A rhombus with diagonals of length 14in and 6 in.
48. A regular octagon with sides of length 8 mm and apothem of 9.7 mm.
49. A regular pentagon with sides length 20 cm and apothem 13.7 cm.
50.
51.
52.
Find the area of the shaded region.
6
53.
Find the area of the shaded region.
54.
55.
56.
Area rectangle=_______
Area triangle=_______
Shaded area=_______
Area rectangle=_______
Area triangle=_______
Shaded area=_______
57.
Area parallelogram=_______
Area rectangle=_______
Shaded area=_______
Match the name of each polygon with the number of sides.
57. Octagon_____
61. Nonagon _____
58. Hexagon _____
62. Pentagon _____
59. Heptagon _____
63. Decagon _____
60. Quadrilateral _____
64. Triangle _____
Classify (Name) the polygon by its number of sides.
65.
66.
67.
Area parallelogram=_______
Area square=_______
Shaded area=_______
A. 3 sides
B. 4 sides
C. 5 sides
D. 6 sides
68.
E. 7 sides
F. 8 sides
G. 9 sides
H. 10 sides
69.
70. How many DIAGONALS from point X does each polygon have?
71. A REGULAR POLYGON has all equal ____________ and all equal __________ Draw and label a regular polygon
with… 3 sides
4 sides
5 sides
6 sides
8 sides
72. Fill in the chart.
Name
Picture
# of
Sides
No picture
n
SUM of Interior
∠’s
EACH interior Angle
Triangle
Quadrilateral
Pentagon
Hexagon
FORMULAS
Memorize them!
7
SUM of Exterior ∠’s
EACH Exterior
Angle
For each regular polygon, find the SUM of the interior angles and the measure of EACH interior angle.
73. Octagon (8 sides)
74. Polygon with 15 sides
75. Polygon with 20 sides
SUM of Interior Angles ____________
SUM of Interior Angles ____________
SUM of Interior Angles ____________
EACH interior angle ____________
EACH interior angle ____________
EACH interior angle ____________
Find the measure of the missing angle.
76.
77.
78.
78.
# of sides___ Sum of Interior ∠’s _____
# of sides___ Sum of Interior ∠’s ____
# of sides___ Sum of Interior ∠’s ____
m∠D =_______
m∠A =_______
m∠D =_______
79.79.
# of sides___ Sum of Interior ∠’s ____
m∠A =_______
Given the SUM of the INTERIOR angles, work backwards to find the number of SIDES in each shape.
80.
720°
81.
1080°
82.
1620°
83.
2880°
For each regular polygon, find the SUM of exterior angles and the measure of EACH exterior angle.
84. Octagon (8 sides)
85. Polygon with 15 sides
86. Polygon with 20 sides
SUM of Exterior Angles ____________
SUM of Exterior Angles ____________
SUM of Exterior Angles ____________
EACH Exterior angle ____________
EACH Exterior angle ____________
EACH Exterior angle ____________
Write an equation and solve for x.
87.
88.
89.
SUM of Exterior Angles ____________
Equation:
SUM of Exterior Angles ____________
Equation:
SUM of Exterior Angles ____________
Equation:
90.
SUM of Exterior Angles ____________
Equation:
Given the measure of EACH EXTERIOR angle in a regular polygon, work backwards to find the number of SIDES.
91. 12°
92. 120°
93. 90°
94. 45°
Classify each figure as CONVEX (“caved out”) polygon, CONCAVE (“caved in”) polygon or Not a Polygon.
95.
96.
97.
98.
8
Ch. 8 CIRCLE Final Exam Review
MATCH the key word with the descriptive phrase.
____1. The set of all point in a plane that are the same distance from a given point
____2. The distance from the center to a point on the circle
____ 3. The distance across the circle, through the center
____4. The distance around a circle
____ 5. The amount of surface covered by a circle
____6. A portion of the AREA of a circle
____7. A portion of the CIRCUMFERENCE of a circle
A. diameter
B. radius
C. circle
D. circumference
E. area
F. arc length
G. area of sector
8. What is the relationship between the radius and the diameter?_______________
9. If the radius is 7 cm, then the diameter is _______
If the diameter is 18 m, then the radius is __________
10. State the FORMULA for CIRCUMFERENCE of a circle: ________________
– NOT 3.14
APPROX: use 3.14 –
Find the exact and approximate CIRCUMFERENCE of each circle. Your answers should have plain units.
11.
12.
13. Diameter = 20 mm
14. Radius = 4 cm
EXACT circumference __________
EXACT circumference __________
EXACT circumference __________
APPROX circumference __________
APPROX circumference __________
APPROX circumference __________
15. A farmer wants to build a circular pen for his
chicken. He wants the radius of his pen to be 25 ft.
Approximately how many feet of fencing would he
need to build the pen?
EXACT circumference __________
APPROX circumference __________
16. A bicycle tire has a diameter of 24 inches. How far
does the tire go in ONE revolution?
(Hint: use circumference formula)
Which formula will you use for fencing? Circumference or Area?
How far does the tire go in 10 revolutions?
Given the CIRCUMFERENCE, work backwards using the formula to find the diameter and radius.
17. Circum= 50
19. Circum = 18.84
20. Circum = 21.98
d = ________ r = _________
d = ________ r = _________
d = ________ r = _________
d = ________ r = _________
21. State the FORMULA for finding ARC LENGTH: ___________________
Use the formula above to find the arc length of AB.
22.
23.
24.
9
25.
26. State the FORMULA for AREA of a circle: ________________
– NOT 3.14
APPROX: use 3.14 –
Find the exact and approximate AREA of each circle. Your answers should have square units.
27.
28.
29. Radius = 3 m
30. Diameter = 8 in.
EXACT area __________
EXACT area __________
EXACT area __________
EXACT area __________
APPROX area __________
APPROX area __________
APPROX area __________
APPROX area __________
Given the AREA, work backwards using the formula to find the radius.
2
31. Area = 36
32. Area =
m2
33. Area = 78.5 ft2
34. Area = 12.56 cm2
35. State the FORMULA for finding the AREA OF A SECTOR: _____________________
Find the area of each sector.
36.
37.
38.
39.
Find the area of the shaded region.
40.
41.
42.
43.
Exact area of big circle:_________
Exact area of square:_________
Exact area of rectangle:________ Exact area of parallelogram:_____
Exact area of small circle:_______
Exact area of circle:_______
Exact area of circle:_______
Area of Shaded region: _________
Area of Shaded region: ______
Area of Shaded region: _______
Exact area of circle:_______
Area of Shaded region: _________
A pizza is cut into 8 congruent pieces as shown. The diameter of the pizza is 16 inches.
44. Find the circumference of the pizza.
46. Find the radius of the pizza.
47. Find the area of the top of the entire pizza.
10
Geometry Final Exam Review – Ch. 9
Name:_________________________________
Hour: ____
Tell whether the solid is a polyhedron. If so, name the solid.
1.
2.
3.
4.
Name the polyhedron. Then count the number of faces and edges.
5.
6.
7.
Name:
Name:
Name:
Faces:
Faces:
Faces:
Edges:
Edges:
Edges:
Use Euler’s formula F + V = E + 2 to find the number of faces, edges or vertices.
8. A prism has 4 faces and 6 edges. How many vertices does it have?
9. A pyramid has 5 faces and 6 vertices. How many edges does it have?
10. A pyramid has 12 edges and 7 vertices. How many faces does it have?
11
Name the solid, then find the surface area to the nearest whole number.
11.
12.
13.
Name:
Name:
Name:
14.
15.
16.
Name:
Name:
Name:
17.
18.
19.
Name:
Name:
Name:
20.
21.
22.
Name:
Name:
Name:
12
Name the solid. Then find the volume of the solid.
23.
24.
25.
Name:
Name:
Name:
26.
27.
28.
Name:
Name:
Name:
29.
30.
31.
Name:
Name:
Name:
32.
33.
34.
Name:
Name:
Name:
13
Geometry Final Exam Review – Ch. 10
Find the value of each expression.
1.
= ____
2.
= ______
Name:_________________________________
Hour: ____
3. 122 = _______
4. 82 = _____
List the perfect squares from 1 to 225
Use the list of perfect squares to simplify each radical…show EXACT answers only. NO DECIMALS!
5.
6.
7.
8.
9.
10.
11.
12.
Use the calculator to find the following rounded to the nearest 100th (two decimal places).
13.
_________
14.
__________
15.
_________
16.
__________
17. State the Pythagorean Theorem: ______________________________ What is it used for?______________________
Can the given side lengths make a right triangle. Answer Yes or No. YOU MUST SHOW WORK!
18.
12, 23, 35
19.
5, 13, 12
20.
Use the Pythagorean Theorem to find the following missing sides. An equation MUST be given. Round to 2
decimals, if necessary.
21.
22.
23.
Equation: ________________ x = _______
Equation: ________________ x = _______
Equation: ________________ x = _______
24.
25.
26.
Equation: ________________ x = _______
Equation: ________________ x = _______
Equation: ________________ x = _______
14
27. A 15-foot ladder is leaning against a wall. It
reaches up the wall 10 feet. How far is the bottom of
the ladder from the wall?
28. A 30-ft wire is attached to an electrical pole. The
wire attaches to a stake on the ground. If the stake is
18 feet from the base of the pole, How tall is the pole?
Equation:
Equation:
29. How long is the hypotenuse of a doorway that is 9
feet by 4 feet?
30. A helicopter flies 9 miles due east and then 6 miles
due south. How far is if from its starting point?
Equation:
Equation:
Can a mattress that is 10 feet long fit through the
doorway?________
Remind yourself of the 45-45-90 and 30-60-90 triangle rules!
45-45-90: hypotenuse = leg
30-60-90: hypotenuse = short leg
Use the special triangle rules to find the missing sides of the following triangles.
31.
32.
33.
x = _______
x = _______
y = ______
34.
x = _______
x = _______
y = ______
35.
y = ______
y = ______
36.
x = _______
y = ______
x = _______
y = ______
37. Us a CALCULATOR set in DEGREE mode to find the following values. Round answers to nearest hundredth.
a) Sin 45 = ________
b) tan 30 = _______
c) cos 90 = ______
d) cos 60 = ______
e) sin 60 = ________
Fill in the ratios for each trig function using the words: opposite, adjacent and hypotenuse.
How do we remember these definitions? _________________________________________
15
For each triangle, give the sin, cos, and tan in fraction form. Find the missing sides where needed and reduce all fractions!
38.
39.
40.
a = ____
sin A_____
sin B_______
sin A_____
sin B_______
sin A_____
sin B_______
cos A______
cos B_______
cos A______
cos B_______
cos A______
cos B_______
tan A ______
tan B ______
tan A ______
tan B ______
tan A ______
tan B ______
Use sin, cos, or tan proportion to solve for the variable.
41.
42.
a = ________
43.
43.
a = ________
44. Donovan leans a 15-ft ladder against the wall. The
ladder makes a 70° angle with the ground. How far up
the building does the ladder reach?
a = ________
45. A tree casts a shadow 25 feet long when the angle
of elevation to the sun is 68°. How tall is the tree?
Use SOH CAH TOA to find the missing ANGLE. Write an equation and use the INVERSE to find the angle measure.
Round to nearest 100th of a degree.
46.
47.
m∠A = ____________
m∠A = ___________
48. Stefan leans a 20-ft ladder against a wall. The
base of the ladder is 3 feet from the wall. What ANGLE
does the ladder make with the ground?
49. Chelsea visited the Washington Monument which
is 550ft tall on her summer vacation. She stood 400
feet away from the base of the monument to take a
picture. At what ANGLE did she need look up to
ensure that she captured the top of the monument in
her picture?
16
Geometry Final Exam Review – Ch. 11
Name: ________________________
Hour: _____
1. How many degrees are in a circle?___________
2. How many degrees are in a semicircle? _____________
Name each of the following for circle O.
3. A semicircle __________
4. Two minor arcs __________ and __________
5. Two major arcs__________ and __________
6. In a circle, the measure of the central angle is the ____________ the measure of the arc.
Find the measure of each angle for each arc of circle P.
7. m∠SPR______________
8.
________________
9.
11 .
________________
________________
10.
________________
12.
________________
13. In a circle, the measure of the inscribed angle is the _____________ the measure of the arc.
14. What is the measure of an angle that is inscribed in a semicircle?________________
Find the measure of the following angles and arcs.
15.
16.
17.
18. What is a tangent segment?_________________
19. What kind of angle is formed when a radius and a tangent meet? ________________
20. If two tangent segments are drawn from a point outside the circle, these segments are ___________
Find the lengths of the following segments.
21.
22.
23.
SR = _____ OT = ______
OC = ____ OB = _____ AB = ____
MT = _________
24. Equal chords mean _________ arcs.
25. If a diameter is perpendicular to a chord, then it_______
the chord and the arc.
17
Using the given picture, find the following lengths.
26. PB = _____________
27. PC = ______________
28. PE = _____________
29. CE = ______________
Note: PD = 5, BE = 2
30. AE = ____________
Draw the following.
31. a triangle inscribed in a square
32. A circle inscribed in a triangle
33. A triangle circumscribed about a
circle
What is the rule for finding the angle in a picture that is Chord-Chord
Find the following angles.
34. m∠1=___________
35. m∠1=_______ m∠2=_________
____________________________
36. m∠1=_______ m∠2=_________
What is the rule for finding the angle in a picture that is tangent-chord
Find the following angles.
37. m∠1=___________
38. m
=_______ m∠1=_________
_______________________
39. m∠1=_______ m∠2=_________
What is the rule for finding angle 1 in each of the following pictures ___________________
Find the following angles.
40. m∠1=___________
41. m∠1=_________
42. m
Write an equation and solve for x.
43.
44.
45.
Equation:________________
Equation:________________
Equation:________________
Answer: _________________
Answer: _________________
Answer: _________________
18
=_______ m∠1=_________