Download Geometry Study guide midterm 1 and more Study Guides, Projects, Research Geometry in PDF only on Docsity!
Cornerstone Exam Study Guide
Subject Geometry
Teacher Mrs. Suh
Length The exam is to be completed within 90 minutes.
Exam
Details
Chapters (Calculator Section)
ü Chapter 2: Logical Arguments and Line Relationships
o Sections 2 - 1 to 2 - 7, Section 2- 9
ü Chapter 3: Rigid Transformations and Symmetry
Chapters (Non-Calculator Section)
ü Chapter 1 : Tools of Geometry
o Sections 1 - 1 to 1- 6
ü Chapter 2 : Logical Arguments and Line Relationships
o Sections 2 - 8 , 2 - 10
Question Types
ü Multiple Choice Question
ü Problem Solving Question
ü Multi-Part Question
Review
Resources
Primary Study Resources
ü Textbook Reading
ü Chapter Resources
ü Chapter Quizzes/Tests
Additional Study Resources
ü Study Guide
Tips
(Before the
Final)
Study Guide
The most important lessons and types of questions for each section have been highlighted in this study
guide. Although a great part of the midterm will mirror the question structure found in this study guide, this
does not provide a comprehensive midterm review.
Terminology
Terms which cannot be defined during the exam have been listed. Concepts that cannot be explained during
the exam have been listed. (Note, however, that this is not an exhaustive list.) A question cannot be
explained during the exam.
Primary Study Resources
In general, you have already studied the primary study resources. When reviewing the primary study
resources, be sure to focus on your previous errors.
Tips
(During the
Final)
Partial Credit
Try to write all the steps. This not only helps you to identify any miscalculation, but it also allows the
teacher to identify any work worthy of partial credit.
Time Management
Focus on questions that are more important (allotted higher points). Skip questions you cannot solve right
away and return to them after going through the rest of the questions..
Section 1-1: Points, Lines, and Planes
Vocabulary collinear
coplanar
intersection
Workbook:
Example 2
a. Name the intersection of the planes O and N.
b. Does 𝐴𝐵
intersect point D? Explain.
Textbook:
Example 1
a. How many different names can be provided for plane N?
b. What would be an unacceptable name for plane N?
c. What would be an unacceptable name for line ℓ?
Problem Multiple Choice. Which statement about the figure below is not true?
A. Point H lies in planes AEG and DEG.
B. Planes ABG , DFG , and BDE intersect at point E.
C. Points A , D , and H are collinear.
D. Points B , E , and F are coplanar.
Section 1-2: Line Segments and Distance
Vocabulary congruent irrational number
Lesson:
Distance
Formula
Workbook:
Example 4
Find the distance between C (–1, 3) and D (3, – 5).
Textbook:
Example 2
What is the value of AB if B is between A and C , AB = 3 x + 2, BC = 7, and AC = 8 x – 1?
Problem If GK = 30, find GH.
Section 1- 3 : Locating Points and Midpoints
Vocabulary midpoint segment bisector
Lesson:
Midpoint
Formula
Section 1- 6 : Two-Dimensional Figures
Vocabulary concave/convex
equilateral/equiangular
regular polygon
perimeter/area/circumference
Lesson:
Polygon Names
of Sides 3 4 5 6 8 10 n
Polygon triangle quadrilateral pentagon hexagon octagon decagon n - gon
Workbook:
Example 1
Name each polygon by its number of sides. Then classify it as convex or concave and regular or irregular.
Textbook:
Example 4
Find the perimeter and area of quadrilateral WXYZ with W (2, 4), X (–3,
3), Y (–1, 0), and Z (3, – 1).
Section 2 - 1 : Conjectures and Counterexamples
Vocabulary inductive reasoning conjecture
Textbook:
Example 1
Write a conjecture that describes the pattern in the sequence. Then use
your conjecture to find the next item in the sequence.
Problem Determine whether the conjecture is true or false. If false , give a counterexample.
Given: Δ ABC , if m Ð A = 60, m Ð B = 60, and m Ð C = 60.
Conjecture: Δ ABC is an equilateral triangle.
Section 2 - 2 : Statements, Conditionals, and Biconditionals
Vocabulary negation
conjunction/disjunction
conditional statement
hypothesis/conclusion
biconditional statement
Lesson:
Related
Conditionals
Workbook:
Example 1
Write a compound statement for each disjunction. Then find its truth value.
p : A diameter of a circle is twice the radius.
q : A rectangle has four equal sides.
a. p ∨ q b. ∽ p ∨ q
Textbook:
Example 6
Rewrite each statement as a biconditional statement. Then determine whether the biconditional is true or
false.
The square of an integer that is divisible by 3 is also divisible by 3.
Section 2 - 3 : Deductive Reasoning
Vocabulary deductive reasoning valid
Lesson:
Law of
Detachment
Lesson:
Law of
Syllogism
Workbook:
Example 1
Determine whether each conclusion is valid based on the given information. If not, write invalid. Explain
your reasoning.
a. Given: Two angles supplementary to the same
angle are congruent. ∠ A and ∠ C are supplementary
to ∠ B.
Conclusion: ∠ A is congruent to ∠ C.
b. Given: If Helen is going to work, then she is
wearing pearls. Helen is wearing pearls.
Conclusion: Helen is going to work.
Textbook:
Example 4
Determine whether the statement is valid based on the information. If not, write invalid.
(1) If a number is prime, then it does not have repeated factors.
(2) If a number does not have repeated factors, then it is not a perfect square.
Conclusion: If a number is prime, then it is not a perfect square.
Textbook:
Example 5
Draw a valid conclusion from the given statements, if possible. Then state whether your conclusion was
drawn using the Law of Detachment or the Law of Syllogism. If no valid conclusion can be drawn, write no
conclusion.
(1) Water can be represented by H 2 O.
(2) Hydrogen (H) and oxygen (O) are in the atmosphere.
Section 2 - 4 : Writing Proofs
Vocabulary postulate (or axiom) theorem
Workbook:
Example 1
Determine whether each statement is always , sometimes , or never true.
a. There is exactly one plane that contains points A , B , and C.
b. Points E and F are contained in exactly one line.
c. Two lines intersect in two distinct points M and N.
Section 2 - 5 : Proving Segment Relationships
Workbook:
Example 1
Write a two-column proof.
Given: Q is the midpoint of 𝑃𝑅
. R is the midpoint of 𝑄𝑆
Prove: PR = QS
Workbook:
Example 2
Write a two-column proof.
Given: 𝐴𝐵
Prove: 𝐴𝐶
Problem The steps below “show” that 1 = 2. Find the error.
Given: a = b
Prove: 1 = 2
Lesson:
Parallel and
Perpendicular
Lines
Textbook:
Example 4
The coordinate system at the right is designed for a soccer field. Each
unit represents one meter. Joe is at point P (35, - 20). The path of the
ball from a corner kick is represented by the equation 𝑦 = −
"
𝑥. To
have the best chance for a shot on goal, Joe wants to run toward the
ball so that his path meets the path of the ball at a right angle. Find an
equation for the line on which Joe should run.
Section 2 - 10 : Perpendiculars and Distance
Lesson:
Distance
Between a Point
and a Line
Workbook:
Example 2
Find the distance between the parallel lines ℓ and m with the equations y = 2 x + 1 and y = 2 x – 4,
respectively.
Textbook:
Example 2
Line n contains points (2, 4) and (–4, – 2). Find the distance between line n and point B (3, 1).
Section 3 - 1 : Reflections
Lesson:
Reflection in the
Coordinate
Plane
Workbook:
Example 1
Construct the image of quadrilateral ABCD under a reflection in line
m.
Workbook:
Example 2
Quadrilateral DEFG has vertices D (–2, 3), E (4, 4), F (3, – 2), and G (–3, – 1). Find the image under reflection
in the x - axis.
Problem Use the diagram at the right. Find the coordinates of the given point
across the given line.
a. A’ , the reflection image of A across y = x
b. A’’ , the reflection image of A’ across y = – x
c. A’’’ , the reflection image of A’’ across y = x
Section 3 - 2 : Translations
Vocabulary translation vector
Lesson:
Translation in
the Coordinate
Plane
Workbook:
Example 2
Rectangle RECT has vertices R (–2, – 1), E (–2, 2), C (3, 2), and T (3, – 1). Graph the figure and its image along
the vector 〈2, – 1 〉.
Problem The graph shown is of the function 𝑦 = 𝑥
$
. Graph and write the
equation of the image after a translation along the vector 〈2, – 1 〉.
Section 3 - 3 : Rotations
Lesson:
Rotations in the
Coordinate
Plane
Workbook:
Example 2
Parallelogram WXYZ has vertices W (–2, 4), X (3, 6), Y (5, 2), and Z (0, 0). Graph parallelogram WXYZ and its
image after a rotation of 270° about the origin.
Problem Rotate 𝑦 =
!
$
𝑥 + 5 about the x - intercept. Write the equation of the image.
