Geometry Final Exam Review – Ch.7Name:______
Hour: ____
SIMPLIFY each ratio completely.
1. = 2. =3. = 4. 32 : 4 =5. 30 : 39 =
Convert units to simplify each ratio.
6. = 7. =8. = 9. =10. =
A basketball team won 12 games and lost 8. Reduce each ratio.11. wins to losses
12. wins to the total number of games played
13. losses to wins
14. losses to the total number of games played / 15. In the diagram, JK : KL is 7 : 2 and JL =36.
Find JK and KL.
Equation:
x = _____ JK = _____ KL = ______
16. Use the triangles to write each ratio in simplest form.
______
______
______/ 17. Use the triangles to write each ratio in simplest form.
= ______ = ______
= ______ = ______
= ______ = ______
Solve these proportions by cross-multiplying. Use the distributive property where needed. Show your work!
18. 19. 8 : 3 = x : 6 20. 21.
Proportion:
Setup a PROPORTION to solve the following problems.
22. If 25Valentine chocolate candiescost $20.00.How much will 42 Valentine chocolates cost?
Proportion:
Answer = ______/ 23. Thomas finished 50 math problems in 20 minutes. At this rate, how many math problems can he do in 30 minutes?
Proportion:
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 ______.
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.Scale Factor: ______
Proportion to find x: Proportion to find y: / 30.
Scale Factor: ______
Proportion to find x: Proportion to find y:
/ 31.
Scale Factor: ______Proportion to find x: Proportion to find y:
32. The two rectangles are similar.
a. Find the scale factor(left to right).
b.Find the ratio of theperimeters of the rectangles. / 33. The scale factor of two similar triangles is 4 : 7, find the ratio of the perimeters.
Determine if the triangles are similar by AA~, SSS~, SAS~, or none. Work must be shown to check proportionsand/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: ______
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:
mT= ______mN = ______mD = ______mT = ______mA = ______
42.43.
"Flipped" or "Twisted" Bow Tie?"Flipped" or "Twisted" Bow Tie?
Proportion to find x: Proportion to find y: Proportion to find x: Proportion to find y:
mP = ______mATC = ______mA = ______m1 = ______mA = ______mE = ______
44. Separate and label triangles here:45.Separate and label triangles here:
Scale Factor: ______Scale Factor: ______
Proportion to find x: Proportion to find y: Proportion to find x: Proportion to find y:
mE = ______mD= ______mF = ______mD = ______mBCA = ______mA = ______
Complete the following proportions by using the picture at the right.
46. ? = ______47. ? = ______
48. ? = ______49. ? = ______
Use a proportion to solve for the missing length.
49. 50.51.52.
Proportion to find x: Proportion to find x: 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 = ______a = ______b = ______y = ______
Geometry Final Exam Review – Ch. 8Name:______
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 7. Draw a rectangle with perimeter 10
and area 8. and area 4.
Converting units. Fill in the blanks.
8. 1 yd = _____ feet9. 2 yd = _____ feet 10. 6 feet = ____ yards 11. 12 feet = ____yards
12. 1 foot = ___ inches13. 5 feet = ___inches 14. 24 inches = ___feet 15. 48 inches = ____ft
16. 1 meter = ____cm17. 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. 25.
26. 27. 28. 29.
Given the dimensions of a parallelogram, find the area.
30. base = 24 cm 31. base = 18 in32. base = 16.2 m33. base = 45 ft
height = 5 cm height = 25 in height = 9.4 m height = 8 yd
Find x for each parallelogram.
34. Area = 48cm235. 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 in242. 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.
Find the area of the shaded region.
Find the area of the shaded region.
Area rectangle=______Area rectangle=______Area parallelogram=______Area parallelogram=______
Area triangle=______Area triangle=______Area rectangle=______Area square=______
Shaded area=______Shaded area=______Shaded area=______Shaded area=______
Match the name of each polygon with the number of sides.
57. Octagon_____61. Nonagon _____A. 3 sidesE. 7 sides
58. Hexagon _____62. Pentagon _____B. 4 sidesF. 8 sides
59. Heptagon _____63. Decagon _____C. 5 sidesG. 9 sides
60. Quadrilateral _____64. Triangle _____D. 6 sidesH. 10 sides
Classify (Name) the polygon by its number of sides.
65.66.67.68.69.
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 / SUM of Interior ∠’s / EACH interior Angle / SUM of Exterior ∠’s / EACH Exterior AngleTriangle /
Quadrilateral /
Pentagon /
Hexagon /
FORMULAS
Memorize them! / No picture / n
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 sides75. 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.
76.77.78.79.
# of sides___ Sum of Interior ∠’s _____ # of sides___ Sum of Interior ∠’s ____ # of sides___ Sum of Interior ∠’s ____ # of sides___ Sum of Interior ∠’s ____
m∠D =______m∠A =______m∠D =______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 sides86. 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.
87.88.89.90.
SUM of Exterior Angles ______SUM of Exterior Angles ______SUM of Exterior Angles ______SUM of Exterior Angles ______
Equation:Equation:Equation: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.
Ch. 8 CIRCLEFinal 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
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: ______
EXACT: use the symbol – NOT 3.14APPROX: use 3.14 – NOT the symbol or the key
Find the exact and approximate CIRCUMFERENCE of each circle. Your answers should have plain units.
11.12.13. Diameter = 20 mm14. Radius = 4 cm
EXACT circumference ______EXACT circumference ______EXACT circumference ______EXACT circumference ______
APPROX 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?Which formula will you use for fencing? Circumference or Area? / 16. A bicycle tire has a diameter of 24 inches. How far does the tire go in ONE revolution?
(Hint: use circumference formula)
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= 5018. Circum = 619. 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.
22.23.24.25.
26. State the FORMULA for AREA of a circle: ______
EXACT: use the symbol – NOT 3.14APPROX: use 3.14 – NOT the symbol or the key
Find the exact and approximate AREA of each circle. Your answers should have square units.
27.28.29. Radius = 3 m30. 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.
31. Area = 36 cm232. Area = 64 m233.Area = 78.5 ft234. 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:______Exact area of circle:______
Area of Shaded region: ______Area of Shaded region: ______Area of Shaded region: ______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.
Geometry Final Exam Review – Ch. 9Name:______
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?
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:
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:
Geometry Final Exam Review – Ch. 10Name:______
Hour: ____
Find the value of each expression.
1. = ____ 2. = ______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, 3519. 5, 13, 1220.
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 = ______
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?Equation: / 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:
29. How long is the hypotenuse of a doorway that is 9 feet by 4 feet?
Equation:
Can a mattress that is 10 feet long fit through the doorway?______/ 30. A helicopter flies 9 miles due east and then 6 miles due south. How far is if from its starting point?
Equation:
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 = ______y = ______x = ______y = ______x = ______y = ______
34.35.36.
x = ______y = ______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? ______
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 = ____
Use sin, cos, or tan proportion to solve for the variable.
41.42.43.
a = ______a = ______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?/ 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 100thof 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?Geometry Final Exam Review – Ch. 11Name: ______
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. ______10. ______
11 . ______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 = ______MT = ______OC = ____ OB = _____ AB = ____
24. Equal chords mean ______arcs.25. If a diameter is perpendicular to a chord, then it______
the chord and the arc.
Using the given picture, find the following lengths.
Note: PD = 5, BE = 2
26. PB = ______27. PC = ______
28. PE = ______29. CE = ______
30. AE = ______
Draw the following.
31. a triangle inscribed in a square32. A circle inscribed in a triangle33. 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=______m∠1=______
Write an equation and solve for x.
43. 44. 45.
Equation:______Equation:______Equation:______
Answer: ______Answer: ______Answer: ______
1