Pre-IB Semester 1 Final Exam Review Sheet 10-11-take 2

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Oct 10, 2013 (3 years and 10 months ago)

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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.