2 Geometry
Final Exam Review
Name: __________________________________________ Period: _________
Chapter 1: Essentials of Geometry
In exercises 6-7, find the midpoint between the two points.
6. T(3, 9) and W(15, 5)
7. C(1, 4) and D(3, 2)
In exercises 8-9, find the distance between the two points.
8. T(3, 4) and W(2, 7)
9. C(5, 10) and D(6, -1)
In Exercises 10-11, use the diagram at the right.
10.
Find x.
11.
Find the m ⦟DEG and m⦟ GEF.
12. The measure of ÐLOM is 21°. OM bisects ÐLON .
a.) What is the measure of ÐLON ?
b.) What is the measure of ÐMON ?
13. A complementary pair of angles have the measurements (x -10) and (2x + 40) Find the measures of each of
the angles.
2 Geometry
Final Exam Review
Chapter 2: Reasoning and Proof
Hypothesis- __________________________________________
Conclusion- __________________________________________
14. Write the converse, inverse and the contrapositive for the given statement.
a.)
If an animal is a frog, then it is an amphibian.
-Converse:
-Inverse:
-Contrapositive:
15. Match the property with the property that it illustrates.
16. Find the values of x and y and each of the four angles in the diagram below.
2 Geometry
Final Exam Review
Chapter 3: Parallel and Perpendicular Lines
17. Classify the pairs of angles as corresponding, alternate interior, alternate exterior, or consecutive interior.
a.) Ð1andÐ8
b.) Ð4andÐ5
c.) Ð2andÐ6
d.) Ð3andÐ5
e.) Ð3andÐ7
f.) Ð3andÐ6
18. Find the value of x.
a.)
b.)
c.)
19. Write an equation of the line that passes through the given point P (-2, 4) and has the slope m = 3.
20.) Write an equation of the line that passes through point P (-1, 1) and is parallel to the equation
y = 2x – 3.
21 & 22.) Write an equation of the line that passes through point P and is perpendicular with the
equation.
a.)
(1, 3), y = 2x – 1
b.)
P(3, 4), y = -1/6x - 10
2 Geometry
Final Exam Review
Chapter 4: Congruent Triangles
By sides: scalene
By angles: acute
isosceles
obtuse
equilateral
right
equiangular
23. Classify the triangle by its side and its angles.
a.)
b.)
c.)
24. Tell whether the triangles can be proven congruent by the given postulate.
a.)
b.)
c.)
25.) Find the value of x. Use the exterior angle theorem
Chapter 5: Relationships with Triangles
26.) Is it possible to construct a triangle with the given side lengths?
a. 4, 11, 15
b. 3, 11, 15
c. 5, 11, 15
27.) A triangle has one side length of 12 and another length of 8. Describe possible side lengths of the third
side.
2 Geometry
Final Exam Review
Chapter 6: Similarity
28.
a.) Write a proportion to show which sides are similar.
b.) Find the value of x.
29) Determine which similarity theorem or postulate proves the triangles below are similar.
Choices: AA Postulate, SSS Similarity theorem, SAS Similarity theorem
a)
b)
30) If ΔAEB ∼ ΔADC, what is the value of AB? ___________ What is the value of AC? _____________
31.) If ΔAEB ∼ ΔADC, what is the value of x? ____________ What is the value of y? _______________
2 Geometry
Final Exam Review
***Chapter 7: Right Triangles and Trigonometry
32.) Label the right triangle with leg lengths 7 and 14. Find the hypotenuse in radical form.
33) Is this a Pythagorean triple 10, 11, 14?
34) Which type of triangle is formed with side lengths 10, 11, 14? (Lesson 7.2)
35) Find the value of x. Write your answer in simplest radical form.
36). Find the value of each variable. Write your answer in simplest radical form.
a.)
b)
c)
d)
37.) Using SOH-CAH-TOA
a) Find cos C.
Find sin C.
b) Find mGH.
2 Geometry
Final Exam Review
Chapter 8: Quadrilaterals
38. Three interior angles of a quadrilateral are 52, 104, and 128. What is the measure of the fourth angle?
39. What is the sum of the interior angles of a regular hexagon? What is the measure of one interior angle of a
hexagon?
**Be able to distinguish between the kinds of quadrilaterals: parallelograms, rhombuses, rectangles, squares,
kites, trapezoids
40. How can you tell the following is a parallelogram?
a)
b)
41. Solve for the values of w, x, y and z in the parallelogram.
42. Solve for x given the following parallelogram?
43. Find m⦟M.
45. Find the midsegment of the trapezoid.
44. Find m⦟G
2 Geometry
Final Exam Review
***Chapter 10: Properties of Circles
46. Use the diagram at the right to label
a) ̅̅̅̅
𝐴𝐺 __________
̅̅̅̅ ___________
b) 𝐴𝐵
̅̅̅̅
c) 𝐶𝐴 __________
d) point B ________
e) ⃡𝐷𝐸 ______________
̂ and m𝑄𝑇𝑆
̂
47. Find m 𝑆𝑇
48. Use properties of tangents to solve for the variable.
a.
b.)
49. Use properties of chords to solve for the variable.
̂ and b) m⦟LMO.
50. Use properties of inscribed angles to find a) m𝐾𝑁
a)
b)
2 Geometry
Final Exam Review
51) Use properties of inscribed polygons to find a) c° and b) m⦟TUV
52. Use angle relationships (see formula sheet) to find a) m⦟1, b) x°, and c) x°
53. Use segment lengths (see formula sheet) to find a) x b) x c) x.
2 Geometry
Final Exam Review
Chapter 11: Measuring Length and Area
54. Find the area of the polygons (use formula sheet).
a.)
c.)
b.
d.)
55. A right triangle has a hypotenuse of 17 cm and a height of 8 cm. Find its area and its perimeter. (Hint: find
the length of the other leg first).
56. Find the circumference and area of a circle with a diameter of 22cm.
57. Find the approximate radius of a circle with a circumference of 90 meters.
58. The area of a rectangle is 100 square units. If the length is 4 times the width, find the value of the length
and the width.
2 Geometry
Final Exam Review
Chapter 12: Surface Area and Volume of Solids
59. Find the surface area of the following geometric solids. (Use formula sheet)
a)
b)
c)
60. Find the volume of the following geometric solids. (Use formula sheet)
a)
b)
d)
e) hemisphere
c)