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IM 2 Semester 2 Review: Final Study Guide (Due 6/9/25)

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Last updated about 2 hours ago
76 questions

Day 1 6/2/25

Main Idea: Geometry Basics

Required
20
Question 1
1.
Use the figure below to answer question. Let m∠MQP= 80.

m∠MQN=_______


m∠NQP=_______
Required
10
Question 2
2.
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6
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6
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6
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6
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6
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6
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6
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6
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6
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6
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35
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10
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10
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10
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10
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10
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10
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10

Day 2 6/3/25

Main Idea: Angles formed by Parallel Lines cut by a Transversal Using Algebra

Required
10
Question 21
21.

Required
10
Required
10
Required
30
Required
30

Main Idea: Sums of the Interior Angles of a Polygon

Required
10
Question 26
26.
Find the sum of the measures of the interior angles in each polygon.

16-gon
_______ degrees

20-gon

_______ degrees

100-gon
_______ degrees
Required
30
Required
15

Main Idea: Interior and Exterior Angles of Polygons

Required
3
Question 29
29.

What is the sum of the exterior angles of any polygon?

Required
3
Required
30
Required
10
Required
10

Main Idea: Angles of a Triangle

Required
15
Question 34
34.
Find each missing angle measures.

m∠1=_______ °
m∠2=_______ °
m∠3=_______ °
m∠4=_______ °
m∠5=_______ °
Required
10
Required
40

Main Idea: Triangle Inequality Theorem

Required
12
Question 37
37.
Given two sides of a triangle, you can set up an inequality using the sum and difference to show the range of possible lengths for the third side:

14 and 22

a) Set up difference and sum that shows the possible range of side lengths for the third side

_______ - _______ <third side (x) <_______ +_______

b) Write the inequality the shows the range of lengths that could be a third side this triangle:

_______ < x <_______
Required
12
Question 38
38.

Day 3 6/4/25

Main Idea: Dilations

Required
10
Question 39
39.
Required
10
Question 40
40.
Required
20
Required
10
Required
10

Main Idea: Creating and Solving Proportions

Required
40
Question 44
44.
Required
15
Required
10
Required
15
Required
15

Main Idea: Ratios and Proportions

Required
10
Question 49
49.
What are the three ways to represent a ratio?

Don't Click This Link

1._______
2._______
3._______
Required
10
Question 50
50.

Use the given ratios to solve each problem:

The ratio of the measures of the three angles in a triangle is 10:3:7. Find the measure of the largest angle.

Main Idea: Similarity

Required
5
Question 51
51.
The pairs of polygons in the example are similar. Give the scale factor of figure A to figure B.

_______:_______
Required
40
Required
5
Required
10

Main Idea: Triangle Proportionality

Required
10
Question 55
55.
Use the Triangle Proportionality Theorem to solve for x.

x=_______
Required
10
Question 56
56.
Required
10

Main Idea: Pythagorean Theorem

10
Question 58
58.
Use the Pythagorean Theorem to find the missing side of the following triangle.

(Round your answer to the nearest tenth.)

x=_______
Required
10
Question 59
59.

Use the Pythagorean Theorem to find the missing side of the following triangle. Leave your answer in simplest radical form.

Main Idea: Right Triangle Similarity

(When you have all 3 Sides of a Right Triangle)

Required
10
Question 60
60.

Solve for x. (Round your answer to the nearest tenth.)

Required
10
Question 61
61.
Solve for x and y. (Round your answer to the nearest tenth.)

x=_______

y=_______

Main Idea: Right Triangle Similarity

Hypotenuse and Leg Theorem

Required
10
Question 62
62.

Solve for x. (Round your answer to the nearest tenth.)

Required
10
Question 63
63.

Solve for x. (Round your answer to the nearest tenth.)

Day 4 6/5/25

Main Idea: Trigonometric Functions

Required
10
Question 64
64.
What is the correct ratio of sides for each trigonometric function?

sin ϴ=_______

cos ϴ=_______

tan ϴ=_______
Required
10
Question 65
65.
Required
10

Main Idea: Properties of Parallelograms

20
Question 67
67.
▱LMNP is a parallelogram.

Solve for x.
_______
What is the length of LM?
_______

M∠P=_______ °
M∠N=_______ °
M∠L=_______ °
Required
30
Required
10

Main Idea: Properties of Rectangles

Required
30
Question 70
70.
If each quadrilateral below is a rectangle, find the missing measures. Do not for get to use the degree symbol in your answers. ( ° )

m∠BCD=_______
m∠ADE=_______
m∠ABD=_______
m∠AEB=_______
m∠CBE=_______
m∠DEA=_______
Required
25
Question 71
71.

Main Idea: Properties of Rhombi

Required
30
Question 72
72.
If each quadrilateral below is a rhombus, use the given information to find the missing measures. Do not for get to use the degree symbol in your answers. ( ° )

m∠KNL=_______
m∠KJL=_______
m∠MLK=_______
m∠JKM=_______
m∠JML=_______
Required
20
Question 73
73.

Main Idea: Properties of Squares

Required
30
Question 74
74.
If the quadrilateral below is a square, find the missing measures.

Do not forget to use the degree symbol in your answers. ( ° )

m∠EFG=_______
m∠GDH=_______
m∠GEF=_______
m∠DHG=_______
Required
20
Question 75
75.

Main Idea: Properties of Trapezoids

Required
15
Question 76
76.
If the quadrilateral below is a trapezoid, find the missing measures.

Find x=_______

Do not forget to use the degree symbol in your answers. ( ° )
m∠VST=_______
If m∠DEG = (5x – 4)°, m∠GEF = (7x – 8)°, m∠DEH = (9y + 5)°, find the value of x and y.

x=_______

y=_______

Main Idea: Naming Angles Formed When Parallel Lines are Cut By a Transversal

Question 3
3.
Name the angle relationship between the two indicated angles in the diagram:


These angles are on__________ side(s) of the transversal and __________ the other two lines. Therefore these angles are __________.
Question 4
4.
Name the angle relationship between the two indicated angles in the diagram:


These angles are on__________ side(s) of the transversal and __________ the other two lines. Therefore these angles are __________.
Question 5
5.
Name the angle relationship between the two indicated angles in the diagram:


These angles are on__________ side(s) of the transversal and __________ the other two lines. Therefore these angles are __________.
Question 6
6.
Name the angle relationship between the two indicated angles in the diagram:



These angles are on__________ side(s) of the transversal and __________ the other two lines. Therefore these angles are __________.
Question 7
7.
Name the angle relationship between the two indicated angles in the diagram:

These angles are on__________ side(s) of the transversal and __________ the other two lines. Therefore these angles are __________.
Question 8
8.
Name the angle relationship between the two indicated angles in the diagram:


These angles are on__________ side(s) of the transversal and __________ the other two lines. Therefore these angles are __________.
Question 9
9.
Name the angle relationship between the two indicated angles in the diagram:

These angles are on__________ side(s) of the transversal and __________ the other two lines. Therefore these angles are __________.
Question 10
10.
Name the angle relationship between the two indicated angles in the diagram:



These angles are on__________ side(s) of the transversal and __________ the other two lines. Therefore these angles are __________.
Question 11
11.
Name the angle relationship between the two indicated angles in the diagram:


These angles are on__________ side(s) of the transversal and __________ the other two lines. Therefore these angles are __________.
Question 12
12.
Name the angle relationship between the two indicated angles in the diagram:

These angles are on__________ side(s) of the transversal and __________ the other two lines. Therefore these angles are __________.

Main Idea: Using Parallel Lines To Find The Measures Of Indicated Angles

Question 13
13.
If m∠1 = 62°, find each measure.


m∠2=_______
m∠3=_______
m∠4=_______
m∠5=_______
m∠6=_______
m∠7=_______
m∠8=_______
Question 14
14.
Given the 2 line are cut by a transversal and are parallel:

What is the measure missing angle?
_______

What is the reason? (Use Notes Page 3 to help you).
_______
Question 15
15.
Given the 2 line are cut by a transversal and are parallel:

What is the measure missing angle?
_______

What is the reason? (Use Notes Page 3 to help you).
_______
Question 16
16.
Given the 2 line are cut by a transversal and are parallel:

What is the measure missing angle?
_______

What is the reason? (Use Notes Page 3 to help you).
_______
Question 17
17.
Given the 2 line are cut by a transversal and are parallel:

What is the measure missing angle?
_______

What is the reason? (Use Notes Page 3 to help you).
_______
Question 18
18.
Given the 2 line are cut by a transversal and are parallel:

What is the measure missing angle?
_______

What is the reason? (Use Notes Page 3 to help you).
_______
Question 19
19.
Given the 2 line are cut by a transversal and are parallel:

What is the measure missing angle?
_______

What is the reason? (Use Notes Page 3 to help you).
_______
Question 20
20.
Given the 2 line are cut by a transversal and are parallel:

What is the measure missing angle?
_______

What is the reason? (Use Notes Page 3 to help you).
_______
If l ∥ m, then solve for x.
Question 22
22.

If l ∥ m, then solve for x.

Question 23
23.

If l ∥ m, then solve for x.

Question 24
24.
Find the value of x.

x=_______

Then, find the measure of each labeled angle.

(6x+20)° = _______ °

(8x)° = _______ °
Question 25
25.
Find the value of x.

x=_______

Then, find the measure of each labeled angle.

(7x+10)° = _______ °

(15x +16 )° = _______ °
Question 27
27.
Find the sum of the measures of the interior angles in each polygon.

(Round your answer to the nearest tenth.)

14-gon
_______ degrees
Each angle is _______

25-gon
_______ degrees
Each angle is_______

85-gon
_______ degrees
Each angle is_______
Question 28
28.
Find the value of x.


x=_______

(8x-1)°=_______
Question 30
30.

What is the formula to find one exterior angle of any polygon?

Question 31
31.
Find the sum of the measures of the exterior angles in each polygon. (Round your answer to the nearest tenth.)

14-gon
_______ degrees
Each angle is _______

25-gon
_______ degrees
Each angle is_______

85-gon
_______ degrees
Each angle is_______
Question 32
32.
Find the value of x and y.

x=_______

y=_______
Question 33
33.
Find the value of x.

x=_______
Question 35
35.

Find the value of x.

Question 36
36.
Find the value:

x=_______ °
m∠D=_______ °
m∠E=_______ °
m∠F=_______ °
Given two sides of a triangle, you can set up an inequality using the sum and difference to show the range of possible lengths for the third side:

31 and 28

a) Set up difference and sum that shows the possible range of side lengths for the third side

_______ - _______ <third side (x)<_______ +_______

b) Write the inequality the shows the range of lengths that could be a third side this triangle:

_______ < x <_______
This is an example of what kind of dilation? _______



Scale factor can be written as (x,y)→(kx, ky)

The scale factor is of this example is (x,y)→ _______
This is an example of what kind of dilation?_______



Scale factor can be written as (x,y)→(kx, ky)

The scale factor is of this example is (x,y)→ _______
Question 41
41.
Graph and label each figure and its image under a dilation with the given
scale factor. Assume all dilations use the origin as the center of dilation.
J': _______
L': _______
K': _______
M': _______
Question 42
42.
Identify the center of dilation and scale factor of each dilation.

center of dilation (x,y)
_______

scale factor
k= _______
Question 43
43.
Identify the center of dilation and scale factor of each dilation.

center of dilation (x,y)
_______

scale factor
k= _______
A music store has 40 trumpets, 39 clarinets, 24 violins, 51 flutes, and
16 trombones in stock.

Write each ratio in simplest form.

trumpets to violins
_______ to _______
write it as a fraction _______

flutes to clarinets
_______ to_______
write it as a fraction_______

trombones to trumpets
_______ to_______
write it as a fraction_______

violins to total instruments
_______ to_______
write it as a fraction_______
Question 45
45.
After cross multiplying this proportion, what is the result? (Round your answers to 2 decimal places.)

_______ = _______


x=_______
Question 46
46.
After cross multiplying this proportion, what is the result? (Round your answers to 2 decimal places.)

_______ = _______

x=_______
Question 47
47.
After cross multiplying this proportion, what is the result? (Round your answers to 2 decimal places.)

_______ = _______


x=_______
Question 48
48.
After cross multiplying this proportion, what is the result? (Round your answers to 2 decimal places.)

_______ = _______


x=_______
Question 52
52.
Use this similarity statement △FGH ~△JKH to list the similar parts.


∠H=∠_______
∠J=∠_______
∠G=∠_______

JH~_______
GH~_______
FG~_______
Question 53
53.
The pairs of polygons in the example are similar. Give the scale factor of figure A to figure B.

_______:_______
Question 54
54.
If △JKL ~ △NMP, find the value of x.
x=_______
Use the Triangle Proportionality Theorem to solve for x.

x=_______
Question 57
57.
Use the Parallel Lines and Proportional Parts to solve for x.

x=_______
Find the 3 trigonometric function for θ, Give each trig ratio as a fraction in simplest form.

sin θ=_______
cos θ=_______
tan θ=_______
Question 66
66.
Find the 3 trigonometric function for θ, Give each trig ratio as a fraction in simplest form.

sin θ=_______
cos θ=_______
tan θ=_______
Question 68
68.
▱ABCD is a parallelogram.

Solve for x.
_______
Find m∠R
_______
Find m∠Q
_______
Question 69
69.

▱STUV is a parallelogram.

If TV = 74 and WV = 4x + 1, solve for x.

If each quadrilateral below is a rectangle, find the missing measures.

VW=_______
WX=_______
YW=_______
ZX=_______
VX=_______
If each quadrilateral below is a rhombus, use the given information to find the missing measures.

x=_______

Do not for get to use the degree symbol in your answers. ( ° )

m∠ADB=_______
m∠BAD=_______
If the quadrilateral below is a square, solve for x and find the missing measures.

x=_______

Do not forget to use the degree symbol in your answers. ( ° )
m∠RQT=_______
m∠PTQ=_______