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December 11, 2014
Geometry-Final Study Guide-Semester 1-2014
For your final on December 16-19, please be ready to show mastery over:
1. Relationships between constructors of geometry including points, lines, planes,
and angles including important vocabulary.
2. Identifying rigid and non-rigid transformations by rule, diagram, and description
and compare them to one another.
3. Identify Similar or Dilated shapes by shortcut, rule, or description.
4. Identify and describe geometric constructions including perpendicular bisector.
5. Identify the results of Rigid Transformations on points on a coordinate plane.
6. Reason what triangle congruency shortcut is used to prove other triangles are
congruent.
7. Reason the relationships given by Similar and Dilated Triangles.
8. Perform a series (compound) of Rigid and Non-Rigid Transformations on a figure
on a Plane.
9. Identify the properties of a Parallelogram.
10. Identify a Series of Rigid Transformations that map one figure onto another on a
Plane.
11. Prove two triangles are congruent to prove additional congruencies or properties
of the shapes.
12. Prove properties of angles and lines within the structure of 2 lines being cut by a
transversal.
Directions: Use the following problems to prepare yourself for the final. There are
ALOT of problems, so be sure that you sample from from each category rather than
spend all your time on just one or two pages.
Notes are not allowed on this final, but think about this...students who took the time
to make or take notes generally do the best...because they took the time to take and
make them NOT because they used them during the test.
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Important Vocab for the Final.
1. Vertical Angles/Vertical Angle Theorem
2. Base Angles/Base Angle Theorem
3. Corresponding
4. Corresponding Angle Postulate, Alternate Interior Angles Theorem
5. Linear Pair Postulate
6. CPCTC
7. SSS, SAS, AAS, ASA, SSA
8. Definition of Supplementary Angles
9. Rigid/Non-Rigid Transformations
10 Parallelogram (properties and stuff)
11. Bisector
12. Perpendicular Bisector
13. Midpoint
14. Preserve
15. Orientation
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1. Relationships between constructors of geometry including points, lines, planes, and angles in
B. If AB is a bisector of <DAC, and AR is a
bisector of <DAB, what is the measure of
m<DAC is 120, what is m<DAR?
A. Sketch <ABC so that m<ABC = 90
Add BD so that BD bisects <ABC
What is m<ABD?
B
C.
A
B
C
D
E
B is a bisector of AE
C is a midpoint of BE
D is bisector of CE
If AC = 18, what is CD? What is BD?
D.
A
C
D
E
F
m<AFE is 150.
FB is a bisector of <AFE
FC is a bisector of <BFE
FD is a bisector of <CFE
What is m<BFD?
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2. Identifying rigid and non-rigid transformations by rule, diagram, and description
and compare them to one another.
Ok, so here's the deal. Problems on the final are taken DIRECTLY from the Khan
Academy recommendation "Qualitatively Defining Rigid Transformations." If you
want to prepare for this section, you have to be able to do these problems. They have
been re-recommended for you.
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3. Identify Similar or Dilated shapes by shortcut, rule, or description.
4. Identify
B and describe geometric constructions including perpendicular bisector.
5. Identify the results of Rigid Transformations on points on a coordinate plane.
8. Perform a series (compound) of Rigid and Non-Rigid Transformations on a figure
on a Plane.
b. Sketch out a series of transformations that will map BROW to
LAMP. Diagram all vectors, lines of reflection, centers and angles
of rotation, and centers and factors of dilation where applicable.
a. Take the figure below through the following
transformations:
R
Step 1: (x, y) --> (-x, y) to take ABC --> A'B'C'
Step 2: Map A'B'C' to A''B''C'' by <-4, 5>
Step 3: Dilate A''B''C'' to A'''B'''C''' by center (0,0) and
scale factor of 2
B
O
M
W
A
P
L
B
A
C
d. Select all of the following descriptions that will map a given
figure onto itself.
y
c. Are the two triangles below Similar? Explain your thinking
regardless of your answer.
1
A
2
x
iv. Reflect over x = 3.5
2
N
ii. Reflect over y- axis
iii. Reflect over Line G
I
Line G
i. Reflect over x-axis
v. Reflect over x = 4.5
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vi. Reflect over y = -1.5
vii. Reflect over y = -4.5
1.5
P
viii. Reflect over the
line through (-1,3) and
(8, -6)
4
C
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Prove: AC = DB
Given: C is the midpoint of BE
<ABC = <DEC
Prove: <CAB = <CDE
Given <1≅<8,
Prove*<4*≅<5
.
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Given:*
BOAT*is*a*parallelogram
Prove:*
A*diagonal*will*cut*it*into*2*congruent*triangles
Given: THIN is a
parallelogram
Prove:
THK =
NIK
H
I
K
T
N
Identify all the definitions and properties of a parallelogram.
-
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Prove
bgf≅ dgf
Given: b and d are midpoints.
c
g
b
a
f
d
e
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