Final
Exam
Information & Review
Problems
Pre

IB
Geometry
2010

2011
Important Information
The final exam will cover Chapters 1
–
13. (Chapter 14 will be covered separately after the final).
The surface area & volume
formulas from page 593 of your book will
be available to you during
the final. You will NOT get your own note card.
The list of theorems below will be available to you during the final
for use in writing proofs
. You
are expected to know what these theorems say
and when to use them as justificat
ions in proofs.
Appendix A of your book lists the theorems and the section in which they are explained.
List of Theorems
Linear Pair Theorem
Vertical Angles Theorem
Parallel Lines and Slopes Theorem
Perpendicular Lines and Slopes Theorem
Corresponding Ang
les Postulate (CAP)
Figure Reflection Theorem
CPCF Theorem (CPCFT)
ABCD Theorem
Alternate Interior Angles Theorem
(AIA)
Isosceles Triangle Base Angles Theorem (ITBAT)
Trapezoid Angle Theorem
SSS, SAS, ASA, AAS, HL Triangle Congruence Theorems
Properties of
a Parallelogram Theorem
Fundamental Theorem of Similarity
SSS, AA, SAS Similarity Theorems
Review Problems
These problems are from the
Chapter Review
of each chapter (NOT the Progress Self

T
est
).
Check answers in the back as you go.
Review problems wil
l be collected for a
25

point
grade on
the day of the final.
Chapter 1
: Sections 1.2, 1.3, 1.6, 1.7, 1.8, Problems
13

17, 19, 35, 37, 39
Undefined terms (point, line, plane)
Difference between a definition, a postulate, and a theorem and how they fit toge
ther to
form geometry
Difference between
,
,
, and
The triangle inequality
Calculating distance
Chapter 2
:
Sections 2.1

2.7
, Problems
1

9 odd, 13,
19, 21, 33, 35, 39, 41
Conditional (If

Then) Statements
Converses of Conditional Statements
Unions and intersections of figures (including
notation)
Names of common polygons
Convexity
Chapter 3
:
3.1, 3.3

3.8,
Problems
1, 9, 11,
17, 23, 35, 53, 55, 59, 61
Definition of, types of, and how to name angles
Definitions of complementary, supplementary, and vertical angles and linear pairs
Linear Pair and Vertical Angle Theorems
Transitive and Reflexive Properties
Parallel lines and ang
les (corresponding, vertical, alternate interior, alternate exterior)
Theorems and postulates related to parallel lines
, transversals, and perpendicular lines
Chapter 4
:
Sections 4.1, 4.2, 4.4

4.7, Problems
5, 7, 11, 17, 19, 23, 30,
31, 41, 42, 51, 53
Def
inition of reflection and how to reflect a figure
Composing reflections, creating rotations and translations from reflections
Definition of isomet
r
ies and how to perform an isometry on a figure (translation,
reflection, rotation, glide reflection)
Magnitud
e and direction of rotations and translations
Properties of isometr
ies
Chapter 5
:
All Sections, Problems 1, 5, 7, 19, 21, 25, 27, 33, 35, 37
Definition of congruence
Using transitive property and definition of reflection as justifications for proofs
Playfa
ir’s Parallel Postulate
Triangle Angle Sum Theorem, Polygon Angle Sum Theorem
Perpendicular Bisector Theorem
Chapter 6
:
Sections
6.1

6.7
, Problems
1, 5,
15
, 17, 27, 29, 41, 43, 45, 46
Definition of symmetry, properties of symmetric figures
Identifying ref
lection and rotation symmetries, lines of reflection and angles of rotation
Isosceles triangle properties and related theorems
Types of quadrilaterals and their properties (including the Quadrilateral Hierarchy)
Properties of kites and trapezoids
Propertie
s of regular polygons
Chapter 7
:
Sections 7.2

7
.9
,
Problems
1

4, 9, 13, 15, 17, 21, 23, 29, 31, 33, 43
Triangle congruence theore
ms (SSS, SAS, ASA, AAS, HL)
Triangle congruence proofs
(including overlapping triangles)
Definition of tessellation and whether
a polygon can tessellate the plane
Properties of Parallelograms
Exterior angle formulas and inequalities
Chapter 8
:
All Sections, Problems
3, 5, 7,
14, 15, 17,
23, 27, 29, 33, 37, 41, 43
Perimeter formulas (polygon, circle)
Area formulas (square, rectan
gle, triangle, trapezoid, parallelogram, circle)
The Pythagorean Theorem and its converse
Arc length, areas of sectors
Chapter
9
:
Sections 9.1
–
9.8
,
Problems 17, 19, 21, 23
Types and definitions of three dimensional figures (prisms, cylinders, pyramids, c
ones,
spheres
)
Plane sections, views and nets of 3

D surfaces
Regular polyhedra
Chapter 10
:
All Sections, Problems 1, 3, 5, 9, 21, 39
Surface and Lateral area formulas (right prisms and cylinders, right cones and pyramids,
spheres)
Volume formulas (
same f
igures as surface area
)
Volumes and surface areas of figures that are combinations of the above figures
Finding volume from surface area and vice versa
Cavalieri’s Principle
Chapter 11
:
Sections 11.1, 11.2, 11.4

11.6, 11.8, Problems 1, 3, 17, 21, 23, 25, 3
1, 35, 39
Negations
How to make the converse, inverse, and contrapositive of a statement
Applying the Laws of Detachment, Contrapositives, Transitivity
Proof by contradiction and indirect proofs
Proofs using coordinate geometry (especially parallel/perpend
icular with slopes)
Distance formula, midpoint formula
Midpoint connector theorem
Chapter 1
2
:
Sections 12.1, 12.2, 12.3, 12.4, 12.5, 12.6 Problems 1, 5, 9, 10, 12, 14, 17, 18, 19, 20,
22,
23,
26
Size

transformations images of figures
Using proportions to f
ind missing parts in similar figures
Apply properties of size

transformations
Use the Fundamental Theorem of Similarity to find perimeters, areas and volumes in
figures
Apply the Fundamental Theorem of Similarity to real life situations
Chapter 13
:
Sectio
ns 13.1, 13.2, 13.3, 13.5, 13.6, 13.7, Problems
15, 21, 31
, 41, 49
Apply the SSS, AA, and SAS Similarity Theorems
Apply the Side

Splitting Theorem
Find missing side lengths with Special Right Triangles (45

45

90 and 30

60

90)
Find missing sides or angles w
ith tangent, sine or cosine ratios and their inverses
NOTE: The above review problems for Chapter 13 REPLACE assignment 82 on the
assignment sheet.
Comments 0
Log in to post a comment