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CHAPTER ONE NOTES
LESSON 1.2, POINTS, LINES, AND PLANES
Point ______________________________
Line ______________________________
Plane ______________________________
Collinear ___________________________
Coplanar ___________________________
Symbol for Line ______________________
Symbol for line segment _______________
Symbol for Ray ______________________
Homework:
__________________________________________________________________
LESSON 1.3, SEGMENTS AND THEIR MEASURE
Segment Addition Postulate
Distance Formula 2D
Distance Formula 3D
Segments that have the same length are called _____________________
and the symbol is ______.
Pythagorean Theorem
Homework:
_____________________________________________________________________
LESSON 1.4, ANGLES AND THEIR MEASURES
An ________ consists of two different rays that have the same
initial point. The rays are the _______ of the angle. The initial
point is the ________ of the angle.
Angle Addition Postulate
Acute
Right
Obtuse
Straight
Two angles are ________________ if they share a common vertex and
side, but have no common interior points (they do not overlap).
Homework:
_____________________________________________________________________
LESSON 1.5, SEGMENT AND ANGLE BISECTORS
The ______________ of a segment is the point that divides, or
___________, the segment into two congruent segments.
Symbol
Midpoint Formula 2D
Midpoint Formula 3D
An __________________ is a ray that divides an angle into two
adjacent angles that are _____________.
Homework:
_____________________________________________________________________
LESSON 1.6 ANGLE PAIR RELATIONSHIPS
Two angles are _________________ if their sides form two pairs of
opposite rays.
Diagram of Vertical Angles
Vertical Angles are always _____________________.
Two adjacent angles are a _______________________ if their non-
common
sides are opposite rays.
Diagram of Linear Pair
Linear Pairs are always _______________________.
Two angles are _______________________ if the sum of their measure
is 90 degrees.
Two angles are _______________________ if the sum of their measure
is 180 degrees.
Homework:
_____________________________________________________________________
LESSON 1.7, INTRODUCTION TO PERIMETER, CIRCUMFERENCE, AND AREA
Perimeter, circumference and area formulas
Square Rectangle
Triangle Circle
Homework:
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CHAPTER TWO
2.1 Conditional Statements
A conditional statement has two parts, a _________________ and a
________________.
When the statement is written in the if-then form, the �if� contains
the _____________ & the �then� contains the _______________.
When you switch the hypothesis and the conclusion, the new
conditional statement is called the _______________________.
When you negate the hypothesis and conclusion of a conditional
statement, you form the ______________________.
When you negate and switch, or switch and negate, you form the
_________________.
Example
Conditional Statement ___________________________________________
Converse ______________________________________________________
Inverse ________________________________________________________
Contrapositive __________________________________________________
2.2 Biconditional Statements
A Biconditional Statement is a statement that contains the
phrase �_____________________�.
For a Biconditional Statement to be true, the conditional statement
and the ____________ must both be true. In other words, you should
be able to read the statement correctly ____________
________________.
Example
Biconditional Statement ________________________________________.
2.3 Deductive Reasoning
Deductive reasoning uses facts, definitions, and accepted properties
in a logical order to write a ___________________
___________________. Deductive reasoning is one of the keys to
success in Geometry.
Law of Detachment. ________________________________________
Example __________________________________________________
Law of Syllogism _____________________________________________
Example _____________________________________________________
It is important to understand the logical argument and to be able to
reason logically on the EOC exam. The names of the laws are less
important.
2.4 Reasoning with Properties from Algebra
This lesson is very important for two reasons. First, it
demonstrates that in Algebra I, you used Deductive Reasoning when
solving basic algebraic equations. You used facts, definitions, and
properties to solve algebraic equations. Second, it uses this
previous knowledge to �bridge� you to Geometric Proofs. In other
words, we will continue to study of Deductive Reasoning in Geometry.
We will end up reusing some of the same properties that you learned
and used in Algebra.
Addition Property _________________________
Subtraction Property _______________________
Multiplication Property ____________________
Division Property _________________________
Reflexive Property ________________________
Symmetric Property _______________________
Transitive Property _______________________
Substitution Property ______________________
Segment Length and Angle Measure Properties
2.5 Proving Statements about Segments
Segment Congruence Properties
Example of Two Column Proof
2.6 Proving Statements about Angles
Angle Congruence Properties
Right Angle Congruence Theorem
Congruent Supplements Theorem
Congruent Complements Theorem
Linear Pair Postulate (critical)
Vertical Angle Theorem (critical)
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Chapter Three Outline
3.1 Lines and Angles
Two lines are parallel lines if they are _____________ and
_____________________.
Two lines are skew lines if they ________________ and
_______________________.
Parallel Postulate
Perpendicular Postulate
*Transversal
___________________________________________________________.
*Corresponding, Alternate Exterior, Alternate Interior, Consecutive
Interior (Same Side)
Lesson 3.2, Proof and Perpendicular Lines
*Flow Proof
Theorem 3.1
Theorem 3.2
Theorem 3.3
Lessons 3.3 & 3.4 Parallel Lines and Transversals Postulate/Theorems
and Converses
Corresponding Angles Postulate
Alternate Interior Angles Theorem
Consecutive Interior Angles Theorem
Alternate Exterior Angles Theorem
Perpendicular Transversal Theorem
Lesson 3.5 Using Properties of Parallel Lines
Theorem 3.11
Theorem 3.12
Lesson 3.6 Parallel Lines in the Coordinate Plane
Slope Bubble Chart
Lesson 3.7 Perpendicular Lines in the Coordinate Plane
Slopes of Perpendicular Lines
Examples:
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Chapter 4 Congruent Triangles
Lesson 4.1Triangles and Angles
Names of Triangles Classified by Sides - ______________,
_______________, & ________________.
Names of Triangles Classified by Angles - ____________,
______________, & _______________ .
Each of the three points joining the sides of a triangle is a
______________.
In a triangle, two sides sharing a common vertex are called
____________________.
In a right triangle, the sides that form the right angle are the
____________.
In a right triangle, the side opposite the right angle is called the
_________________.
(This is always the longest side of a right triangle)
The two congruent sides of an isosceles triangle are called the
______________. The third side is called the __________________.
The sum of the interior angles of a triangle is always
_________________.
The angles that are adjacent to the interior angles are called
________________.
The measure of an exterior angle is equal to the sum of the
_________________________________________________.
The acute angles of a right triangle are __________________________.
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Lesson 4.2, Congruence and Triangles
Two geometric figures are ______________ if they have exactly the
same _______ & __________.
The symbol for congruency is _____________.
When two figures are congruent, there is a correspondence between
their angles and sides such that ________________________ are
congruent and __________________ are congruent.
If two angles of one triangle are congruent to two angles of another
triangle, then _____________________________________________________.
Properties of Congruent Triangles.
Reflexsive
Symmetric
Transitive
Lessons 4.3 & 4.4, Proving Triangles are Congruent
SSS
SAS
ASA
AAS
Lesson 4.5, Using Congruent Triangles
Planning the Proof
a. Draw a Picture
b. Mark it with all given information
c. Mark it with any additional information that you can deduce
d. Look for SSS, SAS, ASA, or AAS
When �Deducing� additional information (the key to your proof), look
for:
a. Common sides
b. Vertical angles
c. Parallel lines cut by a transversal
Lesson 4.6, Isosceles, Equilateral, and Right Triangles
The two adjacent angles of an isosceles triangle are called the
_____________________.
The angle opposite the base of an isosceles triangle is called the
___________________.
If two sides of a triangle are congruent, then the
_______________________________.
If two angles of a triangle are congruent, then the
______________________________.
If a triangle is equilateral, then it is ________________________.
If a triangle is equiangular, then it is _______________________.
There is one additional way to prove triangles are congruent. If
you have a right triangles, and you have congruent hypotenuses and
legs, then the triangles are congruent. This is called the
_________________________________. This is the special case of ASS
that only works for right triangles.
CHAPTER FIVE PROPERTIES OF TRIANGLES
Lesson 5.1, Perpendiculars and Bisectors
Perpendicular Bisector
Theorem 5.1, Perpendicular Bisector Theorem
Theorem 5.2, Converse of the Perpendicular Bisector Theorem
Theorem 5.3, Angle Bisector Theorem
Theorem 5.4, Converse of the Angle Bisector Theorem
HW
___________________________________________________________________
Lesson 5.2, Bisectors of a Triangle
Perpendicular Bisector of a Triangle
Concurrent Lines
Point of Concurrency
Circumcenter of the Triangle
Theorem 5.5, Concurrency of Perpendicular Bisectors of a Triangle
Angle Bisector of a Triangle
Incenter of the Triangle
Theorem 5.6, Concurrency of Angle Bisectors of a Triangle
HW
____________________________________________________________________
Lesson 5.3, Medians and Altitudes of a Triangle
Median of a Triangle
Centroid of the Triangle
Theorem 5.7 Concurrency of Medians of a Triangle
Altitude of a Triangle
Orthocenter of the Triangle
Theorem 5.8, Concurrency of Altitudes of a Triangle
HW
____________________________________________________________________
Lesson 5.4, Midsegment Theorem
Midsegment of a Triangle
Theorem 5.9, Midsegment Theorem
HW
____________________________________________________________________
Lesson 5.5, Inequalities in One Triangle
Theorem 5.10
Theorem 5.11
Theorem 5.12, Exterior Angle Inequality
Theorem 5.13, Triangle Inequality
HW
____________________________________________________________________
Lesson 5.6, Inequalities in Two Triangles
Theorem 5.14, Hinge Theorem
Theorem 5.15, Converse of the Hinge Theorem
HW
___________________________________________________________________
Chapter Six
6.1 Polygons
KNOW THESE NAMES
Number of sides 3 _____________________
Number of sides 4 _____________________
Number of sides 5 _____________________
Number of sides 6 _____________________
Number of sides 7 _____________________
Number of sides 8 _____________________
Number of sides 9 _____________________
Number of sides 10____________________
Number of sides 12 ____________________
Concave ______________________________
Convex _______________________________
All sides are congruent _____________________
All interior angles are congruent ________________
Equilateral and equiangular ___________________
A segment that joins two nonconsecutive vertices _________________
Sum of the interior angles of a triangle is _______________
Sum of the interior angles of a quadrilateral is ___________
HW ____________________________________________________
6.2 Properties of Parallelograms
A _________________ is a quadrilateral with both pairs of opposite
sides parallel.
Theorem 6.2
Theorem 6.3
Theorem 6.4
Theorem 6.5
6.3 Proving Quadrilaterals are Parallelograms
Theorem 6.6
Theorem 6.7
Theorem 6.8
Theorem 6.9
Theorem 6.10
Summary � Proving Quadrilateral are Parallelograms
*
*
*
*
*
*
HW _______________________________________________________
6.4 Rhombuses, Rectangles, and Squares
Venn Diagram
Rhombus
Rectangle
Square
Rhombus Co0rollary
Rectangle Corollary
Square Corollary
Theorem 6.11
Theorem 6.12
Theorem 6.13
HW ___________________________________________________
6.5 Trapezoids and Kites
Trapezoid
Isosceles Trapezoid
Theorem 6.14
Theorem 6.15
Theorem 6.16
Theorem 6.17, Midsegment Theorem for Trapezoids
Theorem 6.18
Theorem 6.19
HW ___________________________________________________
6.6 Special Quadrilaterals
Wire Diagram
Page 367.
HW ______________________________________________________
6.7 Areas of Triangles and Quadrilaterals
Postulate 22 Area of a Square
Postulate 23 Area Congruence
Postulate 24 Area Addition
Theorem 6.20 Area of a Rectangle
Theorem 6.21 Area of a Parallelogram
Theorem 6.22 Area of a Triangle
Theorem 6.23 Area of a Trapezoid
Theorem 6.24 Area of a Kite
Theorem 6.25 Area of a Rhombus
HW ____________________________________________________________
CHAPTER SEVEN � HEAVILY TESTED ON EOC
TRANSFORMATIONS
7.1 Rigid Motion in a Plane
The original figure is called the ________________.
The new figure is called the ___________________.
The three basic types of transformations are the ____________,
_______________,& _________________.
Know the Symbology. ________________________________________.
An _______________ is a rigid transformation as opposed to a
___________ which is non rigid.
HW ___________________________________________
7.2 Reflections
The _________________ is a transformation that acts like a mirror.
The mirror line is called the _________________________.
Reflection in the x-axis. (x,y) is mapped to _____________.
Reflection in the y-axis. (x,y) is mapped to _____________.
Examples:
A figure in the plan has a ________________________ if the figure
can be mapped onto itself by a reflection in the line.
Examples:
HW ___________________________________________________
7.3 Rotation
A ___________ is a transformation in which a figure is turned about
a fixed point.
Fixed point is called the ________________.
How far the object rotates is called the
_______________________________.
Easiest way to do this is to rotate the graph paper and read the
coordinates of the new point(s). We are normally rotating about the
origin.
Examples:
A figure has ______________________if the figure can be mapped onto
itself by a rotation of 180 degrees or less.
Examples:
HW ______________________________________________________
7.4 Translations (Vectors are not on the EOC).
A ______________________ is a transformation that slides your object
across the graph.
Right is plus
Left is minus
Up is plus
Down is minus
Examples:
HW ______________________________________________________
7.5 Compositions
Compositions are simply a combination of transformations.
Examples:
HW _______________________________________________________
Appendix 2, page 864 (VERY IMPORTANT)
Matrix
Dilation � Reduction or Enlargement
Adding and Subtracting Matrices
Representing a Translation
Multiplying Matrices (Recommend you use the Calculator)
Reflection Matrices
Rotation Matrices
HW __________________________________________________________
CHAPTER EIGHT SIMILARITY
8.1, Ratio and Proportion
Ratio
Proportion
Cross Product Property
Reciprocal Property
HW ______________________________________________________________
8.2, Problem Solving in Geometry with Proportions
Additional Properties of Proportions
HW ______________________________________________________________
8.3, Similar Polygons
Similar Polygons
Theorem 8.1
HW _____________________________________________________________
8.4 Similar Triangles
Postulate 25, Angle-Angle Similarity Postulate
HW ______________________________________________________________
8.5, Proving Triangles are Similar
Theorem 8.2, SSS Similarity Theorem
Theorem 8.3, SAS Similarity Theorem
HW __________________________________________________________________
8.6, Proportions and Similar Triangles
Theorem 8.4, Triangle Proportionality Theorem
Theorem 8.5, Converse of the Triangle Proportionality Theorem
Theorem 8.6, Three Parallel Lines Theorem
Theorem 8.7, Angle Bisected Theorem
HW __________________________________________________________________
8.7, Dilations
Dilation
Reduction
Enlargement
HW __________________________________________________________________
CHAPTER NINE RIGHT TRIANGLES AND TRIGONOMETRY INTRODUCTION
Lesson 9.1, Similar Right Triangles
Theorem 9.1 Similar Right Triangles
Theorems 9.2 & 9.3 Geometric Means
HW ___________________________________________________________
Lesson 9.2 & 9.3 Pythagorean Theorem
Theorem 9.4 Pythagorean Theorem
Pythagorean Triples
Theorem 9.5 Converse of the Pythagorean Theorem
Theorem 9.6, Pythagorean Inequality
Theorem 9.7, Pythagorean Inequality
HW ______________________________________________________________
Lesson 9.4, Special Right Triangles
Theorem 9.8, 45/45/90
Theorem 9.9, 30/60/90
HW _________________________________________________________________
Lesson 9.5 Trigonometric Ratios
Sine
Cosine
Tangent
SOH-CAH-TOA
Angle of Elevation/Angle of Depression
HW __________________________________________________________________
Lesson 9.6 Solving Right Triangles
Sine Inverse
Cosine Inverse
Tangent Inverse
HW
___________________________________________________________________
Note: You will not see Trig again until AFM or Precalculus
CHAPTER 10, CIRCLES
Lesson 10.1, Tangents to Circle
Chord Segment �
Secant Line �
Tangent Line �
Theorem 10.1, Line Tangent to Circle
Theorem 10.2, Line Perpendicular to Radius
Theorem 10.3, Two Segments that are Tangential
HW ________________________________________________
Lesson 10.2, Arcs and Chords
Central Angle �
Minor Arc �
Major Arc �
Measure of Minor Arc �
Measure of Major Arc �
Postulate 26, Arc Addition Postulate -
Theorem 10.4, Congruent Minor Arcs -
Theorem 10.5, Diameter Perpendicular to Chord -
Theorem 10.6, Chord as Perpendicular Bisector �
Theorem 10.7, Congruent Chords �
HW _________________________________________________
Lesson 10.3, Inscribed Angles
Inscribed Angle �
Intercepted Arc �
Theorem 10.8, Measure of Inscribed Angle �
Theorem, 10.9, Same Arc �
Inscribed -
Circumscribed -
Theorem 10.1, Inscribed Right Triangle -
Theorem 10.11, Inscribed Quadrilateral �
HW ____________________________________________________
Lesson 10.4, Other Angle Relationships in Circles
Theorem 10.12, Tangent/Chord �
Theorem 10.13, Two Chords �
Theorem 10.14, Tan/Sec �
Theorem 10.14, Two Tan �
Theorem 10.14, Two Sec �
HW ________________________________________________________
Lesson 10.5, Segment Lengths in Circles
Theorem 10.15, Two Chords �
Theorem 10.16, Two Secants �
Theorem 10.17, Secant/Tangent �
HW ________________________________________________________
Lesson 10.6, Equations of Circles
Standard Equation of a Circle
HW __________________________________________________________
CHAPTER 11, AREA OF POLYGON AND CIRCLES
Lesson 11.1, Angle Measures in Polygons
Theorem 11.1, Polygon Interior Angles theorem
Corallary to Theorem 11.1
Theorem 11.2, Polygon Exterior Angles Theorem
Corallary to Theorem 11.21.2008
HW __________________________________________
Lesson 11.2, Areas of Regular Polygons
* Theorem 11.3, Area of an Equilateral Triangle
Theorem 11.4, Area of Regular Polygon
HW __________________________________________
Lesson 11.3, Perimeters and Areas of Similar Figures
Theorem 11.5, Areas of Similar Polygons
HW __________________________________________
Lesson 11.4, Circumference and Arc Length
Theorem 11.6, Circumference of a Circle -
Corollary, Arc Length Corollary -
HW __________________________________________
Lesson 11.5, Areas of Circles and Sectors
Theorem 11.7, Area of a Circle
Theorem 11.8, Area of a Sector
HW __________________________________________
Lesson 11.6, Geometric Probability
Geometric Probability
Probability and Length
Probability and Area
HW __________________________________________
CHAPTER 12
SURFACE AREA AND VOLUME
Lesson 12.1, Exploring Solids
A _______________ is a solid that is bounded by polygons, called
_____________.
An ________________ of a polyhedron is a line segment formed by the
intersection of two faces.
A ______________ of a polyhedron is a point where three or more
edges
meet.
Another name for vertex is a ________________.
Types of Solids
Prism
Pyramid
Cone
Cylinder
Sphere
A polyhedron is ________________ is all of its faces are congruent
regular polygons.
The intersection of a plane and a solid is called a ___________
______________.
Platonic solids
Tetrahedron
Octahedron
Dodecahedron
Icosahedron
Euler�s Theorem
HW __________________________________________________________
Lesson 12.2, Surface Area of Prisms and Cylinders
A ______________ is a polyhedron with two congruent faces, called
___________, that lie in parallel planes.
The other faces, called __________________, are parallelograms
formed
by connecting the corresponding vertices of the bases.
In a __________________, each lateral edge is perpendicular to both
bases.
Prisms that have lateral edges that are not perpendicular to the
bases are _____________.
The _______________ of a polyhedron is the sum of the areas of its
faces.
The _______________ of a polyhedron is the sum of the areas of its
lateral faces.
Surface Area of a Right Prism
Surface Area of a Right Cylinder
HW __________________________________________________________
Lesson 12.3, Surface Area of Pyramids and Cones
A __________ is a polyhedron in which the base is a polygon and he
lateral faces are triangles with a common vertex.
A _______________ has a regular polygon for a base and its height
meets the bases at its center.
Surface Area of a Regular Pyramid
Surface Area of a Right Cone
HW __________________________________________________________
Lesson 12.4, Volume of Prisms and Cylinders
Volume of a Cube
Cavalieri�s Principle
Volume of a Prism
Volume of a Cylinder
HW __________________________________________________________
Lesson 12.5, Volume of Pyramids and Cones
Volume of a Pyramid
Volume of a Cone
HW __________________________________________________________
Lesson 12.6, Surface Area and Volume of Spheres
Surface Area of a Sphere
Volume of a Sphere
HW __________________________________________________________
Lesson 12.7, Similar Solids
Similar Solids Theorem
HW __________________________________________________________
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