THIS PACKET IS POSTED ON THE WEBSITE – IT’S CALLED “FINAL EXAM REVIEW”
Remember this divider?! You can expect questions from me on these topics. Use past quizzes,
tests, and the practice questions in this packet to prepare for the final exam.
The topics below will be assessed on the multiple-choice section of the final exam; it is your responsibility
to study these topics! For all topics, you should have notes and classwork to refer to. Additionally, I have
listed additional resources below.
Unit
Topic #
Topic
Congruence
1
CPCTC
Additional resources:
Quiz 4.2
Congruence
2
Congruence Postulates
Quiz 4.3
Congruence
3
Triangle Proofs
Quiz 4.3
Congruence
4
Triangle Proofs to prove other things
Quiz 4.3
Area and 3D Figures
5
Calculating Area
Quiz 5.1
Area and 3D Figures
6
Composite Area
Quiz 5.1
Area and 3D Figures
7
Calculating Volume
Quiz 5.2
Area and 3D Figures
8
Composite Volume
Quiz 5.2
Area and 3D Figures
9
Real Life Questions
Posters
Area and 3D Figures
10
Rotations
Quiz 5.3
Area and 3D Figures
11
Cross Sections
Quiz 5.3
Similarity
12
Proportional Sides
Quiz 6.1
Similarity
13
Congruent Angles
Quiz 6.1
Similarity
14
AA Proofs
Quiz 6.2
Similarity
15
Triangles with Parallel Lines
Quiz 6.2
Similarity
16
Area and Volume of Similar Figures
Similarity Project
Trigonometry
17
Pythagorean Theorem
Google it!
Trigonometry
18
Identifying Ratios
Quiz 7.1
Trigonometry
19
Finding Sides
Quiz 7.1
Trigonometry
20
Finding Angles
Quiz 7.1
Trigonometry
21
Law of Sines
Pre-Quiz 7.2
Trigonometry
22
Law of Cosines
Pre-Quiz 7.2
1
What will be provided to you on the final exam:
Law of Sines:
Law of Cosines:
Some things you need to know:
 CPCTC = Corresponding Parts of Congruent Triangles are Congruent
 SAS, SSS, ASA and AAS are congruence postulates (these rules prove triangles congruent
 Area formulas:
o Circle: 𝐴 = 𝜋𝑟 2
o Square: 𝐴 = 𝑠 2
o Rectangle: 𝐴 = 𝑙𝑤
o Parallelogram: 𝐴 = 𝑏ℎ
o Triangle: 𝐴 =
𝑏ℎ
2
o Trapezoid: 𝐴 = (

𝑏1 +𝑏2
2
)ℎ
Volume formulas (remember that B = area of the base)
o Prism/Cylinder: 𝑉 = 𝐵ℎ
o Pyramid/Cone: 𝑉 =
𝐵ℎ
3
4
o Sphere: 𝑉 = 3 𝜋𝑟 3












In similar figures, angles are congruent
In similar figures, sides are proportional. All sides are multiplied by the same scale factor.
In similar figures, areas are multiplied by the square of the scale factor.
In similar figures, volumes are multiplied by the cube of the scale factor
Triangles can be proved similar using AA (Angle-Angle)
A line parallel to one side of the triangle creates two similar triangles (remember the strategy of
redrawing the overlapping triangles as two separate triangles).
The Pythagorean Theorem is 𝑎2 + 𝑏 2 = 𝑐 2 . It can only be used in right triangles. The c is the
hypotenuse.
SOH CAH TOA can only be used in right triangles.
What goes in these parentheses is always an angle measure: 𝑆𝑖𝑛( )
Law of Sines and Law of Cosines can be used in any triangle, lowercase letters represent side lengths,
uppercase letters represent angle measures.
Law of Sines: Use in problems involving two angles and two sides
Law of Cosines: Use in problems involving one angle and three sides.
2
Final Exam Review Questions
Topic #1: CPCTC
Topic #2: Congruence Postulates
̅ and ∠𝐻 ≅ ∠𝐾.
Given: J is the midpoint of 𝐼𝐿
What is the method of proof that could be used
to prove ∆𝐻𝐼𝐽 ≅ ∆𝐾𝐿𝐽?
In the diagram below ∆𝐴𝐵𝐶 ≅ ∆𝑋𝑌𝑍. Which
statement must be true?
A.
B.
C.
D.
E.
∠𝐶 ≅ ∠𝑌
̅̅̅̅ ≅ ̅̅̅̅
𝐴𝐶
𝑌𝑍
̅̅̅̅
̅̅̅̅
𝐶𝐵 ≅ 𝑋𝑍
∠𝐴 ≅ ∠𝑋
∆𝐵𝐶𝐴 ≅ ∆𝑍𝑋𝑌
A.
B.
C.
D.
SAS
AAS
SAS
ASA
Topic #3: Triangle Proofs
̅̅̅̅ bisects ∠𝐴𝐵𝐶, ̅̅̅̅
Given: 𝐷𝐵
𝐴𝐵 ≅ ̅̅̅̅
𝐵𝐶
Prove: ∆𝐴𝐵𝐷 ≅ ∆𝐶𝐵𝐷
Statements
Reasons
3
Topic #4: Triangle Proofs to prove other things
̅̅̅̅, ∠𝐴 ≅ ∠𝐶
Given: E is the midpoint of 𝐷𝐵
̅̅̅̅ bisects ̅̅̅̅
Prove: 𝐷𝐵
𝐶𝐴
Statements
Reasons
Topic #5: Calculating Area
Topic #6: Composite Area
What is the area, in square units, of trapezoid
QRST shown below?
The largest possible circle is to be cut from a 10foot square board. What will be the approximate
area, in square feet, of the remaining board
(shaded region)?
A.
B.
C.
D.
4
20
30
50
80
Topic #7: Calculating Volume
Topic #8: Composite Volume
Find the volume of the figure below. Round to the nearest
tenth.
Find the volume of the figure below. Round to the nearest
tenth.
Topic #9: Real Life Questions
The sphere at the top of a water tower holds enough
water to pressurize the water supply for the city. The
radius of the sphere measures 12 yards. Throughout
the day, the sphere lost 4157.3 cubic yards of water.
If the sphere was completely full at the beginning of
the day, about how much water is left in the sphere
at the end of the day? (Use 3.14 for 𝜋 and round to
the nearest tenth.)
Topic #10: Rotations
What figure will be created when rectangle ABDC is
̅̅̅̅?
rotated about 𝐵𝐷
5
Topic #11: Cross Sections
Topic #12: Proportional Sides
A tree that’s 8 feet tall casts a shadow that’s 12 feet
long. How tall is a tree that casts a shadow that’s 33
feet long?
What is the intersection of a plane and a sphere
through its center?
A. Circle
B. Semi-circle
C. Ellipse
D. Sphere
Topic #13: Congruent Angles
If ∆𝐴𝐵𝐶~∆𝑋𝑌𝑍, 𝑚∠𝐴 = 23°, and 𝑚∠𝐵 = 57°,
what’s the measure of 𝑚∠𝑍?
Topic #14: AA Proofs
Construct the proof below.
Given: DE GH
Prove: ∆𝐹𝐺𝐻~∆𝐹𝐷𝐸
Statements
6
Reasons
Topic #15: Triangles with Parallel Lines
̅̅̅̅ . If AB = 4, BC = 10 and EB
̅̅̅̅ ∥ 𝐶𝐷
In the diagram, 𝐸𝐵
= 6, what’s CD?
Topic #16: Area and Volume of Similar Figures
A tank has a volume of 32m³. It is enlarged with
scale factor 3. What is the volume of the enlarged
tank?
The area of a rectangle is 36 𝑖𝑛2 . What would be the
new area if I increased the length and width by a
scale factor of 4?
Topic #17: Pythagorean Theorem
Topic #18: Identifying Ratios
George rides his bike 12 km south and then 14 Give the ratio for 𝑠𝑖𝑛(𝑍).
24
km west. How far is he from his starting
a.
32
point?
24
a. 7.4 km
b.
40
b. 18.4 km
c.
c. 26.0 km
d. 40.6 km
d.
7
32
40
40
24
Topic #19: Finding Sides
Topic #20: Finding Angles
Find the value of x.
Find the measure of the indicated angle.
a. 41°
b. 49°
c. 57°
d. 65°
a. 12.2
b. 16.1
c. 18.5
d. 21.3
Topic #21: Law of Sines
Topic #22: Law of Cosines
Find e. Round to the nearest tenth.
In ∆𝐽𝐾𝐿, 𝐽𝐾 = 5.3, 𝐾𝐿 = 7.1, and 𝑚∠𝐿 = 42.
To the nearest degree, what is 𝑚∠𝐽?
a. 42
b. 64
c. 67
d. 90
8
Mixed Practice
Find the volume of the figure below.
If ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐹. Find 𝑚∠𝐸𝐷𝐶.
A.
B.
C.
D.
E.
20 cm
32 cm
35°
67°
78°
A 40-foot ladder leans against a building,
making a 60° angle with the flat ground. To
the nearest foot, what is the distance from
the building to the base of the ladder?
a. 20
b. 23
c. 69
d. 80
9
At the store, Newton finds the total volume of soda in
a pack is 351.68 cubic inches. If each cylinder-shaped
can has a height of 7 inches and a diameter of 4
inches, how many soda cans are in a pack? (Use 3.14
for π.)
Calculate the area of the shaded region. Round to the
nearest tenth.
Given: ̅̅̅̅
𝐶𝐴 and ̅̅̅̅
𝐷𝐵 bisect each other
Prove: ∆𝐷𝐸𝐶 ≅ ∆𝐵𝐸𝐴
Statements
Reasons
10