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A practice test for a Geometry course. It includes questions related to equilateral triangles, conditional statements, angle measures, congruent triangles, and prime numbers. Each question is linked to a video tutorial on the internet. The test includes multiple-choice and open-ended questions. suitable for students who want to practice for an upcoming Geometry exam or review the course material.
Typology: Exams
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Day 1
Write your answer on the line.
(Related Tutorial Video: Video 1)
find a counterexample.
If you have a dog, then you are a pet owner.
0 A. If you are a pet owner, then you have a dog. True
0 B. A dog owner owns a pet. True
0 C. If you are a pet owner, then you have a dog. False, you could have a hamster.
0 D. If you have a dog, then you are a pet owner. False, you could have a hamster.
(Related Tutorial Video: Video 1)
(Related Tutorial Videos: Video 1, Video 2, Video 3)
Day 2
Write your answer on the line.
(Related Tutorial Videos: Video 1, Video 2)
6x + 3
7.5x
10x – 5
What is the value of x? ______ 2 _________
What is the measure of angle 2? ______50°_________degrees
Equilateral means all three sides are congruent, so
one possible equation might be:
Original Statement: If P , then Q
Converse Statement: If Q, then P
′
Joanna drew this figure and said “The diagonals of this figure bisect each other, so it must be a square.”
Joanna made an error in her mathematical argument. What is the error?
0 A. There is no error. The figure Joanna drew is a square.
0 B. In the figure Joanna drew, the diagonals do not bisect each other.
0 C. Joanna used the converse of the teacher’s statement and the converse is false.
0 D. Joanna’s teachers statement is false. The diagonals of a square do not bisect each other.
(Related Tutorial Video: Video 1)
(Related Tutorial Videos: Video 1, Video 2)
The vertical diagonal is not bisected. Bisecting a
line segment means the segment is separated into
two congruent pieces.
Midpoint Formula: (
𝑋 1
+𝑋 2
2
𝑌 1
+𝑌 2
2
Midpoint: (
− 1 + 6
2
2 + 8
2
Midpoint: (
5
2
Midpoint: ( 2
1
2 ,
Day 4
What theorem or postulate can you use to prove ∆𝐾𝐿𝑀 ≅ ∆𝑁𝐿𝐽?
0 A. Corresponding Parts of Congruent Triangles are Congruent
0 B. Side-Angle-Side Congruence
0 C. Angle-Side-Angle Congruence
0 D. Side-Side-Side Congruence
(Related Tutorial Video: Video 1, Video 2, Video 3)
at point Q.
Determine the coordinates of point Q.
You may use the blank grid to help determine the solution.
Write your answer on the line.
What are the coordinates of point Q****? ( __ 1 ___ , __- 2 ___ )
(Related Tutorial Videos: Video 1, Video 2
𝑚 < 𝐾𝐿𝑀 ≅ 𝑚 < 𝑁𝐿𝐽 (Vertical angles are congruent)
Since the diagonals of a square bisect
each other, point Q will be the midpoint
of either of the diagonals. Find the
midpoint of the line segment joining
points ( 3 , 1 ) & (− 1 , − 5 )
Day 6
0 A. The diagonals bisect pairs of opposite angles.
0 B. The diagonals are congruent.
0 C. The diagonals bisect each other.
0 D. The diagonals are perpendicular
(Related Tutorial Video: Video 1)
Determine the m∠ EBC.
Write your answer on the line.
What is the m ∠ EBC****? ____ 40 _____ °
(Related Tutorial Videos: Video 1, Video 2 )
“If a figure is a pentagon, then it has five sides”
Which statement is the inverse?
0 A. If a figure has five sides, then it is a pentagon.
0 B. If a figure is a pentagon, then it does not have five sides.
0 C. If a figure does not have five sides, then it is not a pentagon.
0 D. If a figure is not a pentagon, then it does not have five sides.
(Related Tutorial Videos: Video 1, Video 2)
The diagonals of a rhombus are perpendicular
bisectors of each other, so 𝑚 < 𝐵𝐸𝐶 = 90°
Original Statement: If P , then Q
Inverse Statement: If NOT P , then
Day 7
What is the m∠ J?
(Related Tutorial Videos: Video 1, Video 2)
Fill in the blanks for steps 5 and 6 to complete the proof.
Given: B is the midpoint of 𝐴𝐸
B is the midpoint of 𝐶𝐷
Prove: ∆𝐴𝐵𝐷 ≅ ∆𝐸𝐵𝐶.
Statements Reasons
. 1. Given
. 3. Given
Definition of midpoint
m Day 9
Look at the diagram.
Determine the values for a and b that would make the quadrilateral a parallelogram.
0 A. a = 13.5, b = 166.
0 B. a = 16.7, b = 93.
0 C. a = 13.5, b = 106
0 D. a = 16.7, b = 86.
(Related Tutorial Video: See question 16 )
Determine the length of y. Express your answer in simplified radical form.
Write your answer on the line.
What is the length of y****? 6 √ 5
(Related Tutorial Video: Video 1)
Which statement is true?
0 A. Line m and line n are perpendicular.
0 B. Line m and line n are parallel.
0 C. Line m and line n will intersect.
0 D. Line m and line n are skew
Opposite angles in a parallelogram are
congruent. Therefore, 6 𝑎 − 7 = 4 𝑎 + 20
Angle Measure: (6)(13.5)-7=74°
Consecutive angles in a parallelogram are
supplementary (add up to 180°). Therefore,
Line l
Line m
Line n
Day 10
Use a trigonometric ratio (sine, cosine, tangent) to determine how high Mary climbed.
Be sure to write the equation and show the steps you used to solve the equation. Round your answer to the
nearest foot.
(Related Tutorial Videos: See question 7 , Video 1)
1 km ≈ 0.62 mi
(Related Tutorial Videos: Video 1, Video 2)
0 A. M is a midpoint of AB. Therefore AM = MB.
0 B. Squares have equal sides. This figure has equal sides, therefore this figure is a square.
0 C. The base angles of an isosceles triangle are equal. The base angles of this triangle are equal.
Therefore, this triangle is isosceles.
0 D. Triangular numbers have a pattern. 1, 3, 6, 10, and 15 are triangular numbers. Therefore, the next
triangular number is 21.
(Related Tutorial Videos: See question 12 )
100 feet
Height climbed
Horizontal distance
sin 11 .9° =
sin 11. 9
How high did Mary climb?≈ 20. 6 𝑓𝑒𝑒𝑡
How many miles will a person run during a 5-kilometer race? 3. 1 𝑚𝑖𝑙𝑒𝑠
Inductive Reasoning: Based on observation and
predictions.
Day 12
(Related Tutorial Video: Video 1)
is false, find a counterexample.
“Two angles measuring 180 degrees are supplementary”
0 A. Two angles not measuring 180 degrees are supplementary. True
0 B. More than two angles measuring 180 degrees are non-supplementary. True
0 C. Non-supplementary angles are not two angles measuring 180 degrees. True
0 D. Non-supplementary angles are two angles measuring 180 degrees. False; supplementary angles
must measure 180 degree.
(Related Tutorial Videos: See question 18 )
Figure # of edges
e
f
v f + v
Triangular Pyramid 6 4 4 8
Triangular Prism 9 5 6 9
Square Pyramid 8 5 5 10
Cube 12 6 8 14
Hexagonal Pyramid 12 7 7 14
Hexagonal Prism 18 8 12 20
(Related Tutorial Videos: Video 1, Pyramid Definition, Prism Definition)
cos =
cos 𝐼 =
Original Statement: If P , then Q
Contrapositive: If not Q , then not P
Day 13
0 A. Four congruent sides.
0 B. Diagonals bisect the angles.
0 C. Diagonals are perpendicular.
0 D. Four right angles.
(Related Tutorial Video: Video 1, Video 2)
Write your answer on the line.
(Related Tutorial Video: Video 1)
0 A. Reflected over the x-axis.
0 B. Reflected over the y-axis.
0 C. Reflected over the line y = – x.
0 D. Reflected over the line y = x.
(Related Tutorial Video: Video 1)
Day 14
(Related Tutorial Videos: Video 1, Video 2)
x
The ratio for a 30°-60°-90° triangle are:
𝐾𝐽
̅̅̅
𝑤𝑖𝑙𝑙 𝑏𝑒 𝑡𝑤𝑖𝑐𝑒 𝑎𝑠 𝑏𝑖𝑔 𝑎𝑠 𝐾𝐻
̅̅̅̅
𝐾𝐽
̅̅̅
= ( 2 )( 5 ) = 10
30°
60°
(Related Tutorial Video: See question 18 )
0 A. isosceles
0 B. scalene
0 C. equilateral
0 D. right
(Related Tutorial Videos: See question 5 )
Write the inverse.
The point that does not bisect a segment is not the midpoint
Determine if the statement is true or false. ____________TRUE_________________________
If it is false, write a counterexample.
= 𝟔 𝒖𝒏𝒊𝒕𝒔 (by counting)
2
2
2
2
2
2
2
2
∆RTS is Isosceles
Day 16
𝐴𝐷̅̅̅̅ is not parallel to 𝐵𝐶̅̅̅̅
Draw and label a shape that satisfies all of the given information.
Determine the most specific name for the shape.
What is the most specific name for quadrilateral ABCD****? Isosceles Trapezoid
(Related Tutorial Video: Video 1)
1 inch = 2.54 centimeters
Determine the volume of the calculator box to the nearest cubic centimeter.
Write your answer on the line.
What is the volume of the calculator box
to the nearest cubic centimeter? ≈ 𝟒𝟕𝟓. 𝟐𝟐 𝒄𝒎
𝟑
(Related Tutorial Video: Video 1)
(Related Tutorial Video: Video 1)
3
literally means 29 (𝑖𝑛)(𝑖𝑛)(𝑖𝑛)
The conversion looks like:
3
(x, y) (x + 3, y – 5)
Day 18
1
2
feet tall. Michael measures his shadow as 8 feet long. A tree in his backyard has a shadow
that is 25 yards long. How tall is the tree?
0 A. 51.56 yards
0 B. 17.19 feet
0 C. 51.56 feet
0 D. 36.36 yards
(Related Tutorial Video: Video 1)
Which statement is true?
0 A. The triangles are congruent.
0 B. The triangles are similar but not congruent.
0 C. The triangles are not similar or congruent.
0 D. There is not enough information to determine similarity or congruence.
(Related tutorial Videos: See question 10 )
vegetable garden was 24 cubic feet. He built another garden box that was two times longer and two times
higher. He thinks the volume will be twice as much.
Explain why Steven is not correct.
Set up a proportion:
𝑀𝑖𝑐ℎ𝑎𝑒𝑙
′
𝑠 𝐻𝑒𝑖𝑔ℎ𝑡
𝑀𝑖𝑐ℎ𝑎𝑒𝑙𝑠 𝑆ℎ𝑎𝑑𝑜𝑤
𝑇𝑟𝑒𝑒 𝐻𝑒𝑖𝑔ℎ𝑡
𝑇𝑟𝑒𝑒 𝑆ℎ𝑎𝑑𝑜𝑤
Using cross products we find the tree’s height=
have to convert the yards to feet by multiplying by the
conversion factor of
3 𝑓𝑒𝑒𝑡
1 𝑦𝑎𝑟𝑑
, which gives us ≈ 51. 56 𝑓𝑒𝑒𝑡
x
y
z
Volume =
2x
y
2z
Volume=( 2 𝑥)(𝑦)( 2 𝑧) = 4 𝑥𝑦𝑧
By doubling 2
dimensions, Steve has
actually increased the
Volume by a factor of 4
If Steven wants his second garden box to have twice the volume, what should he do instead?
(Related Tutorial Video: See question 51 )
Day 19
(Related Tutorial Video: Video 1, See question 7 )
(Related Tutorial Video: Video 1)
1 and
3 are congruent.
(Related Tutorial Video: See question 3 )
If Steve wants to double the volume he should consider only doubling one dimension…so
Make the box twice as long
Make the box twice as high
Make the box twice as wide
Increase all three dimensions by a factor of √
3
tan 𝐺 =
tan
− 1
tan 𝐺
= tan
− 1
