Name:___________________________________________________Period:_________Date:____________________
Chapter 1:
Vocabulary: Know and understand the following terms. Use your notes to help you.
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conjecture
counterexample
point
line
plane
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collinear
coplanar
line segment
ray
angle
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acute angle
right angle
obtuse angle
straight angle
vertical angles
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linear pair
complementary
angles
supplementary
angles
 Be able to find and describe patterns.
1. Predict the next three numbers in the sequence -5, -2, 4, 13, …
 Know how to use the segment postulates.
2. Suppose J is between H and K. Use the Segment Addition Postulate to solve for x.
𝐻𝐽 = 2𝑥 + 5
𝐽𝐾 = 3𝑥 − 7
𝐾𝐻 = 23
 Know how to write a conjecture.
3. Look at the following set of equations and write a conjecture based upon your
observations.
Conjecture: _______________________________
_____________________________________________
____________________________________________.
 Be able to provide a counterexample for a conjecture.
4. If x² = 25, then x = 5
Counterexample:
 Know how to use the Distance Formula to measure distances.
Distance Formula:
̅̅̅̅. Simplify your answer.
5. Use the Distance Formula to find the length of segment 𝐴𝐵
A(3,0), B(8, 10)
 Be able to identify points, lines, planes, rays, segments, etc. using proper notation
6.
 Use the Midpoint Formula to find the point that bisects a segment.
Midpoint Formula:
̅̅̅.
6. Find the coordinates of the midpoint of segment 𝐽𝐾
J(-1, 7), K(3, -3)
 Be able to use properties of angle bisectors to find missing angle measures.
⃗⃗⃗⃗⃗
𝐸𝐹 is the angle bisector of ∠𝑇𝐸𝐴. Find any angle measures not given in the diagram.
7. a.
b.
 Be able to use the properties of vertical angles, linear pair angles, and supplementary
angles to find missing angle measures
a.
b.
c.
d.
 Classify different types of angles.
8. Find the measure of the angle and fill in the blanks with acute, obtuse, right, or
straight.
a.
mABE  ______ . It is a(n) _______________________________ angle.
b. mGBE  _______ . It is a(n) _______________________________ angle.
c.
mGBD  _______ . It is a(n)_______________________________ angle.
d. mABG  _______ . It is a(n) _______________________________ angle.
 Identify complementary and supplementary angles.
Complementary angles sum to ____________. Supplementary angles sum to _____________.
9. a. ∠𝐴 and ∠𝐵 are supplementary.
Find 𝑚∠𝐴 and 𝑚∠𝐵.
𝑚∠𝐴 = 5𝑥 + 2
𝑚∠𝐵 = 9𝑥 + 10
b. A and B are complementary.
Find mA and mB .
A  3x  15
mB  2x
Chapter 2:
Vocabulary:
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hypothesis
conclusion
converse
inverse
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contrapositive
biconditional
statement
perpendicular lines
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Law of Detachment
Law of Syllogism
 Know how to write a conditional statement in if-then form. Also know how to find the
converse, inverse, and contrapositive of a conditional statement.
10. Conditional Statement: Three points are collinear if they lie on the same line.
If-Then:
Converse:
Inverse:
Contrapositive:
 Recognize and use biconditional statements.
11. Can the statement be written as a true biconditional statement?
A rectangle is a square if it has four congruent sides.
 Use symbolic notation to represent logical statements.
12. Let p be “the car will start” and q be “the battery is charged.” Write the symbolic
statements in words.
 𝒑→𝒒

~𝒒

~𝒒 → ~𝒑
 Form conclusions by applying the laws of logic (Law of Syllogism or Law of
Detachment) to true statements.
13. Use the Law of Syllogism to write the statement that follows from the pair of true
statements.
If the sun is shining, then it is a beautiful day.
If it is a beautiful day, then we will have a picnic.
14. Use the Law of Detachment to write a conclusion from the pair of true statements.
If I study for my geometry final, then I will pass.
I study for my geometry final.
 Use properties of algebra.
Solve the equation and state a reason for each step.
15. Statements
26𝑢 + 4(12𝑢 − 5) = 128
Reasons
 Prove statements about congruent angles and segments.
16. Use the given information to complete the missing reasons in the proof.
Given: ∠𝐴 ≅ ∠𝐵, ∠𝐵 ≅ ∠𝐶
Prove: ∠𝐴 ≅ ∠𝐶
Statements
Reasons
1.
1.
2. 𝑚∠𝐴 = 𝑚∠𝐵
2.
3
3. Definition of congruent angles.
4. 𝑚∠𝐴 = 𝑚∠𝐶
4.
5.
5.
Chapter 3:
Vocabulary:
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parallel lines
skew lines
parallel planes
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transversal
corresponding angles
alternate interior angles
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alternate exterior angles
same side interior angles
 Identify angles formed by transversals.
Identify the relationship between the angles in the diagram.
17. ∠1 and ∠2
18. ∠2 and ∠3
19. ∠1 and ∠4
20. ∠1 and ∠5
21. ∠4 and ∠2
22. ∠5 and ∠6
 Identify parallel lines, perpendicular lines, skew lines, and parallel planes
23. Use the diagram to answer the following:
a. a pair of parallel lines
b. a pair of skew lines
c. a pair of perpendicular lines
d. a pair of parallel planes
 Prove and use results about parallel lines and transversals.
24. Find the value of x.
(2𝑥 + 5)°
(6𝑥 + 15)°
25. Find the value of x that makes 𝑝 ∥ 𝑞.
p
80°
(2𝑥 + 20)°
q
 Find slopes of lines.
Slope Formula:
26. Find the slope of the line through the points (-1, -2) and (-6,-4).
 Use slope to identify parallel and perpendicular lines.
Parallel lines have _______________________________________ slopes.
Perpendicular lines have ________________________________________ slopes.
A line parallel to a line with slope 5 has slope _____________.
A line perpendicular to a line with slope 5 has slope ______________.
 Be able to determine and explain if lines are parallel by looking at their angle
relationships.
27.
Parallel? Yes/No
Parallel? Yes/No
Why?
Why?
 Write equations of parallel and perpendicular lines.
1
28. The line parallel to 𝑦 = − 4 𝑥 + 5 with a y-intercept of 7.
29. The line perpendicular to 𝑦 = −3𝑥 + 2 and that passes through the point (0,6).
Chapter 4:
Vocabulary:
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equilateral triangle
isosceles triangle
scalene triangle
acute triangle
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equiangular triangle
right triangle
obtuse triangle
hypotenuse
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legs of a triangle
base angles
vertex angles
 Identify triangles as equilateral, isosceles, scalene, equiangular, acute, right, or obtuse.
30. Classify the following triangles by their angles and their sides.
a.
b.
c.
 Know how to use the Triangle Sum Theorem and Exterior Angle Theorem.
Triangle Sum Theorem:
Exterior Angle Theorem:
 Understand the Base Angles Theorem and Converse for isosceles triangles.
31. Find the value of x in the following figures.
a.
b.
 Know the triangle congruence postulates and theorems and when to use them.
They are:
32. What congruence postulate or theorem can you use to prove the triangles are
congruent? If it is not possible, write “not enough information.”
a.
b.
c.
d.
e.
f.
33. Prove that ABC  FDE .
Statements
Reasons
1.
1.
2.
2.
3.
3.
4.
4.
Name________________________
Geometry Final Exam Information/
Study Guide
Your Final Exam is designed to take around 90 minutes and will cover everything up to and
including triangle proofs. A few things to keep in mind:
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Vocabulary is there for you to refer to. You don’t have to define every word but you do
need to be prepared to know the definition of these words. I would suggest going
through Haiku, notes, asking me or making flash cards if you don’t know these words.
The practice problems are required to get the completion points on the study guide. I
expect that you are showing your work and treating these questions like you would on a
test.
Please don’t check the study guide key (that will be posted Friday) until you are done
with the study guide. Checking your work after you do the study guide can help you
focus on skills that you need help on.
DUE DATE
Weds (5/20)
Fri (5/22)
Final Exam Day
HAVE DONE:
Chapter 1
Chapter 2
Everything!
2
2
15
YOUR SCORE:
POINTS
For checkpoints, the following will determine your grade:
2 points- Assigned section completed with shown work
1 point- Assigned section partially complete and/or limitations with shown work
0 point- Little to none of the section completed.
HELP: Mr. Benzel will be delighted to help you Tuesdays and Thursdays after school as long as
you get to OHs by 4:15. If those dates are a problem, you can email Mr. Benzel before hand and
schedule an appointment with him.