Geometry Midterm Review Guide
To prepare for your midterm exam, please follow these suggested steps. The more practice you
do, the better prepared you will be for the exam. Be sure to have your calculator with
WORKING batteries, a WORKING compass, and a WORKING protractor with a ruler, and
more than one sharpened pencil. Do not expect to borrow materials.
1. Review key vocabulary terms at the beginning of each chapter or use the list at the end of the
chapter in the review.
2. Read the chapter summary at the end of each chapter several times. Write down any ideas that
are unclear.
3. Review the quizzes and tests you have already taken and be sure that you would get 100% if you
took the same test today.
4. Complete the lesson-by-lesson review in the Study Guide and Review section at the end of
each chapter.
5. Complete the practice test at the end of each chapter.
6. Use pages 969-980 for extra practice problems for each section of each chapter. This is the
EXTRA PRACTICE section of the back of your book.
7. Use pages 999-1003 for extra practice word problems for each section of each chapter. This is
the MIXED PROBLEM SOLVING section of the back of your book.
8. For additional practice on areas you may use previous homework assignments and worksheets.
These should be a solution key to check your work.
9. Use the guiding questions in the remainder of this packet for a general review. However, do not
rely solely on these questions.
*REMINDER: We did the following sections:
Chapter 1 sections 1.1 - 1.7 (just vocab in 1.6 and 1.7)
Chapter 4 section 4.7
Chapter 9 sections 9.1 - 9.6
Chapter 2 sections 2.5 - 2.8
Chapter 3 sections 3.1, 3.2, 3.5
Chapter 4 sections 4.1-4.6
Chapter 5 section 5.1 - 5.3, 5.5, 5.6
Chapter 6 sections 6.1 - 6.6
Chapter 1
What are the 3 undefined geometric terms?
What is a point and how is it labeled? A line? A plane? Give a real world example of each.
What does collinear mean? Coplanar? Draw a picture depicting each.
If a point is between two other points, what would that tell you? Draw a diagram.
What is the difference between being the midpoint and a point being between?
What are the 2 distance formulas?
What is the distance between (2, -1) and (-3, 5)? Write the radical in simplest form.
What is the distance on a number line between 7 and -12?
What are the 2 midpoint formulas?
What is the midpoint of the segment with endpoints (2, -1) and (-3, 5)?
What is the segment on a number line with endpoints 7 and -12?
What is an angle formed by? Draw an angle that is 100 degrees, label the sides and the vertex,
and then correctly name the angle.
What three words would classify an angle by its measure? Draw a pic of each.
Identify/draw an example of adjacent angles, linear pairs, vertical angles, complementary,
supplementary angles.
What are the criteria for a figure to be a polygon?
Draw an example of a concave polygon and a convex polygon.
What does it mean for a polygon to be REGULAR?
L
Chapter 9
1. A congruence transformation is also know as a(n) ___________________.
A
2. How do you perform a regular reflection? Do this one.
C
3. How do you bounce a ball off a wall using reflections?
B
4. What about on the coordinate plane over the x-axis? Over the y-axis?
F
E
G
5. How do you do a regular translation? Do this one.
6. What about on a coordinate plane with vector <a, b>?
V
7. When doing a regular rotation, which direction do you rotate?
J
P
8. How do you perform a regular rotation? Rotate ∆JKL about point P 105 .
K
9. What about on a coordinate plane for a rotation of 90, 180, or 270 degrees?
L
10. What does it mean to do a composition of transformations? Will they be congruent?
11. What is it called when you do a translation and then a reflection?
12. If you were to reflect a figure two times over two intersecting lines, what is the short cut?
Over parallel lines? And how do you know how much to move the figure?
13. What is a tessellation? Give 3 real world examples.
14. What are the two types of 2D symmetry we learned about? Give real world examples.
15. What is the order of symmetry and what is the magnitude of symmetry?
16. What are the two types of 3D symmetry we learned about? Give real world examples.
17. How do you perform a regular dilation? Do this one with a k = 3 and center D.
M
18. If AB = 5 and A’B’ = 15, what is the scale factor?
N
D
O
Chapter 2
What can we conclude about complementary angles? Supplementary? Vertical? Right? Know
these angle theorems.
What is the difference between a postulate and a theorem?
Be familiar with algebraic proofs, geometric proofs, proving segment relationships, proving
angle relationships, and the point, line, plane postulates.
Prove: If 2x + 5 = 21, then x = 8.
Chapter 3
Describe parallel lines, parallel planes, and skew lines.
Draw two parallel lines cut by a transversal. Identify a pair of alternate interior, alternate
exterior, consecutive interior and corresponding angles. What can you conclude about each pair
of angles?
What theorems prove lines are parallel?
Chapter 4
Classify triangles by its sides and angles. Draw some examples.
The three interior angles of a triangle add up to __________________
Draw an example that demonstrates the exterior angle theorem.
Draw 2 congruent triangles. State all the congruent PARTS and write a congruence statement.
What does it mean to be congruent?
What are the 6 ways we can prove two triangles congruent? Which ones don’t prove?
After you prove triangles are congruent, how do you prove that all of its parts are congruent?
Make a conclusion using the isosceles triangle theorem. Make a conclusion using the converse.
If you have an equilateral triangle, name three conclusions you can make about the triangle.
Chapter 5
How are each formed and what do the theorems allow you to conclude:
Circumcenter,
Incenter,
Centroid,
Orthocenter
What is the difference between the Perp Bis Thm and its converse?
What is the difference between the Angle Bis Thm and its converse?
What does the Angle Side Thm say?
What does the Exterior Angle Ineq Thm say?
How do you know if three side lengths can form a triangle?
Given 2 side lengths, how do you find the range of the third side?
What do you need to have in order to use the Hinge Thm/Converse and what does it prove?
Chapter 6
1. What is the formula find the sum of the interior angles of a n-sided convex polygon?
2. Find the sum of the interior angles of a regular convex hexagon. Then, find the measure of
each angle.
3. What is the sum of the exterior angles of a convex polygon?
4. What is the sum of the exterior angles of a regular 20-gon?
5. What is the definition of a parallelogram? Draw a diagram.
6. What does the Properties of a Parallelogram Thm say? Draw diagrams.
a)
b)
c)
d)
7. Describe the differences between the situations of when you would use the defn of
parallelograms to prove something versus Properties of a Parallelogram Thm.
8. What does the Diagonals of Parallelograms Thm say?
a)
b)
9. What is the formula for finding the distance between 2 points on the coordinate plane?
10. What is the formula for finding the midpoint between 2 points on the coord plane?
11. What does the Conditions for a Parallelogram Thm say? Draw diagrams.
a)
b)
c)
d)
12. Describe the differences between the situations of when you would use the Conditions for a
Parallelogram Thm to prove something versus Properties of a Parallelogram Thm.
13. What is the definition of a rectangle? Draw a diagram.
14. What does the Diagonals of a Rectangle Thm say? And the converse?
15. Is a rectangle a parallelogram? _______ Is a parallelogram a rectangle? _______
16. What is the definition of a rhombus? Draw a diagram.
17. What is the definition of a square? Draw a diagram.
18. What does the Diagonals of a Rhombus Thm say? Draw a diagram.
a)
b)
19. Is a rhombus a parallelogram? ______ Is a square a parallelogram?______
Is a square a rhombus? _________ Is a square a rectangle? _________
20. What does the Conditions for a Rhombus and Square Thm say? Draw a diagram.
a)
b)
c)
d)
21) What is the definition of a trapezoid? Draw a diagram and label the parts.
22) What is the definition of an isosceles trapezoid? Draw a diagram.
23) What does the Isosceles Trapezoid Thm say?
a)
b)
c)
24) What is the midsegment of a trapezoid? Draw a diagram.
25) Is a midsegment on only isosceles trapezoids or on any trapezoid? ________________
26) What is the formula to find the length of the midsegment (Trapezoid Midseg Thm)?
27) What is the definition of a kite? Draw a diagram.
28) What does the Kite Thm say?
a)
b)
29) Is a rhombus a kite? __________ Is a kite a parallelogram? ___________
Formulas:
Midpoint
Distance
Sum of interior angles of convex polygon
Midsegment
Pythagorean Thm
CONSTRUCTION:
Copy segment / angle
Parallel lines.
Segment / angle bisector
Perpendicular bisector of a segment.
Be familiar with the following terms to use in proofs (you may add more to this list):
Reflexive property
Consecutive interior angles
theorem/converse
Symmetric property
Corresponding angles postulate/converse
Transitive property
Exterior angle theorem
Substitution Property
Triangle Sum Thm
Distributive property
Defn of congruence
Addition/subtraction/division/multiplication
props
CPCTC
Defn of angle bisector
Third angles theorem
Defn of segment bisector
SSS, SAS, AAS, ASA, HL Cong Post/Thm
Def of midpoint (Midpoint Thm)
Isosceles triangle theorem/converse
Defn of complementary/supplementary
Exterior Angle Inequality Thm
Defn of perpendicular
Triangle Ineq Thm
Point Line Plane Postulates (2.1-2.7)
Hinge Thm/Converse
Vertical angles theorem
Defn of Perp Bis
Supplement theorem
Defn of Parallelogram, rectangle, rhombus,
square, kite, trapezoid, isosceles trap
Complement theorem
Props of parallelogram Thm
Congruent supplements theorem
Diags of parallelogram thm
Congruent complements theorem
Segment addition postulate
Angle addition postulate
Conditions for a parallelogram thm/
Conditions for a rhombus and a square thm
Diags of rectangle thm/ Diags of rhombus
thm
Right angle theorems
Isosceles Trapezoid Thm
Alternate interior angles theorem/converse
Trap Midsegment Thm
Alternate exterior angles theorem/converse
Kite Thm