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Name: _______________________________________
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Date: _______________
Name: _______________________________________
In the exercises below , use the diagram to the right.
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Find the indicated length.
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Find the length of the segment. Leave answer in simplest radical form.
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Find the midpoint of the segment.
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Solve for the indicated angle measure.
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m ABD
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Area and Reasoning
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32. Using the diagram below, that represents a kitchen floor, answer the following questions.
a. What is the area of the kitchen?
b. If the floor is to be tiled, how many tiles would be needed if the tiles are 1/3 ft squares?
c. If a package of 15 tiles costs $8.99, how much would it cost to tile the kitchen?
13 feet
3 feet
6 feet
8 feet
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Write a two column algebraic proof.
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Choose the best answer for each multiple choice question.
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Name: _______________________________________
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Chapter 3: Parallel and Perpendicular Lines
Use the figure at the right to answer the following questions.
1.) Name a line parallel to CD . ______________
2.) Name a line skew to CD . _______________
3.) Name a line perpendicular to CD . ____________
4.) Name a plane parallel to ABC. ______________
5.) Name a plane perpendicular to ADE. _____________
Use the figure at the right to answer the following questions.
6.) Classify the pair of angles:  3 and  7
7.) Classify the pair of angles:  4 and  5
8.) Classify the pair of angles:  3 and  6
9.) Classify the pair of angles:  4 and  7
10.) Find the measure of the numbered angles in the figure below.
m 1 = _______
m 2 = _______
115o 1
2 3
m 3 = _______
m 4 = _______
4
6
m 5 = _______
m 6 = _______
m 7 = _______
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Name: _______________________________________
Date: _______________
11.) Find the value of x and y.
110o
(3y - 20)o
(2x + 50)o
12.) Find the value of x that makes m || n.
(7x - 12)o
(2x + 33)o
m
n
13.) Find the value of x that makes m || n.
m
(4x + 33)o
(3x + 70)o
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Name: _______________________________________
Date: _______________
14.) Find the slope of the line that passes through the points (2 , -4) and (-6 , 2).
15.) Find the slope of the line that passes through the points (-3 , 7) and (-3 , 18)
16.) Find the slope of a line parallel to the line 2x + 3y = 7.
17.) Find the slope of a line perpendicular to the line 7x + y = 14.
Write equations to Parallel and Perpendicular Lines
18.) Find the equation of the line parallel to the line 2x - 4y = 3 passing through the point (4 , 8).
19.) Then find the equation of the line perpendicular to the line x - 3y = 3, passing through
the point (4, 8).
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Name: _______________________________________
Chapter 4: Congruent Triangles
1.) What is m W if m X = 59o and m XYZ = 137o.
2.) Find
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What is the value of n?
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What is the measure of
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Name: _______________________________________
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Classify the following triangles by their angles.
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60o
40o
60o
60o
70o
70o
Classify the following triangles by their sides.
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Find the measure of  A in each of the triangles below.
A
C
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12.)
30o
72o
A
B
B
13.) Find the value of x.
4x - 26
x + 43
50o
50o
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Name: _______________________________________
Date: _______________
14.) Which of the following is NOT a triangle congruence postulate?
A.) Side-Side-Side
B.) Side-Angle-Side
C.) Angle-Side-Angle
D.) Side-Side-Angle
Fill in the correct statements for each proof for each of the following.
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Given:  D and  E are right angles.
GF bisects DE
Prove: DHG  EHF
Statements
Justifications
(1)
(1) Given
(2)
(2) Definition of Right Angles
(3)
(3) Given
(4) DH  HE
(4)
(5)
(5)
(6) DHG  EHF
(6)
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Name: _______________________________________
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Date: _______________
Given: AD || CD
DB  CB
Prove: ADB  ECB
Statements
Justifications
(1)
(1) Given
(2)  D   C
(2)
(3)
(3) Given
(4)
(4)
(5) ADB  ECB
(5)
Sketch the 5 triangle congruency theorems and show how you would use them on the triangle.
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Name: _______________________________________
Date: _______________
Chapter 6: Similarity
Answer the following questions. Find x or the ?.
(1)
(2)
(3)
(4)
(5)
(6)
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Name: _______________________________________
Date: _______________
7. Name the type of transformation shown.
8. Use a reflection in the y-axis to draw the other half of the figure.
9. Figure ABC has vertices A (–3, 3), B (1, –1), and C (0, 5). Sketch ABC in pen and draw its image after the translation
(x, y) → (x – 1, y + 2)
(x, y) → (x – 1, y + 1)
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Name: _______________________________________
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State the triangle that represents the image: 90° clockwise rotation of HGC about point J.
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State the segment that represents the image: 90° counterclockwise rotation of MG about point J.
You can use tracing paper to help you see the rotation.
12. Figure ABC has vertices A (–3, 3), B (1, –1), and C (0, 5). Sketch ABC in pen and draw its image after the translation.
(x, y) → (x + 1, y – 2)
(x, y) → (x + 4, y + 2).
13. Write the coordinate translation that moves each figure on the coordinate plane. (2 pts)
figure 1  figure 2
(x, y) 
figure 3 figure 4
(x, y) 
figure 3 figure 2
(x, y) 
figure 4  figure 2
(x, y) 
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Name: _______________________________________
Date: _______________
Chapter 7: Right triangles
Solve each variable.
(1)
(2)
(3)
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x
8
(4)
(5)
(6)
(7)
(8)
(9)
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Name: _______________________________________
Date: _______________
Chapter 7: World Problems using Right Triangles
10. A 25 ft tree has a support rope tied to its top and secured to the ground, 40 feet from the base of the
tree. If the rope is 50 feet long, can you justify if the tree is perpendicular to the ground? You must
support your answer with at least two sentences and mathematical reasoning?
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MATHEMATICAL WORK:
11. The home owner wants to place a support beam diagonally between two legs of his deck. If the
legs are 12 feet tall and 8 feet apart, how long of a support beam will he need?
Support beam
12. Find the height of an equilateral triangle that has side lengths of 8 inches. Round answer to
the nearest hundredth. Sketch the figure.
13. Find the perimeter of the rectangle at the right.
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Name: _______________________________________
Date: _______________
14. A 24 foot ladder is available to help reach the top of a 15 foot wall. If the state regulations
are that the ladder must make a 30 degree angle with the ground, where on the wall will the
ladder reach? Construct a viable argument and support your answer with mathematical
computations.
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15. Use the Geometric Mean to solve for the variable(s).
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