Answers to Chapter 3.3that are not answered in the book
Short hand fallacy key for chapter 3.3:
Appeal to Unqualified Authority = UA
Hasty Generalization = HG
False Cause = FC Slippery Slope = SS
If there is no fallacy = None
Section I. 1. HG 3. UA 4. SS
Chapter 3, Section 1
Lines & Angles
Definitions
Skew Lines: Do not intersect & are not coplanar
Parallel Lines: never intersect and are coplanar
Parallel Planes: planes which do not intersect
Parallel Postulate
If there is a line & a point not on the line
Chapter 2, Section 4
Properties
Subtraction: If a=b, then a-c=b-c
Multiplication: If a=b, then ac = bc
Addition: If a=b, then a+c=b+c
Division: If a=b and c0, then ac=bc
Additional Properties
Reflexive: For any real number a = a.
Symmetric: If a = b, then
Chapter 2, Section 1
Conditional Statement
Also know as an If-then statement.
If its Monday, then I will go to school.
Hypothesis: its Monday
Conclusion: I will go to school
Converse
When you switch the hypothesis & conclusion in a conditional statement.
Chapter 1, Section 1
Patterns & Inductive Reasoning
Conjecture
An unproven statement that is based on observation.
Look at the figure or statement & prove that its true or false.
Example: All odd numbers can be expressed as the sum of two
prime numbers.
3
Chapter 1, Section 4
Angles & Their Measures
Parts of an Angle
The endpoint they share is called the vertex.
The two rays are called the sides.
An angle can be named by its vertex alone or 3 points.
An angle is made up of two rays which have a common endp
Chapter 7, Section 1
Rigid Motion in a Plane
Definitions
Transformations is moving the preimage to becoming the image.
Preimage: The original figure.
Image: the new image after the transformation.
Isometry: is a transformation which doesnt change the leng
Chapter 6, Section 1
Polygons
Describing a Polygon
An enclosed figure (all segments)
Two segments meet @ a point called a vertex
Each segment is called a side.
Identifying a Polygon
Number of Sides are indicative of the name
Quadrilateral
Pentagon
Hexagon
Chapter 4, Section 1
Triangles & Angles
Naming a Triangle
Equilateral: all sides are congruent
Isosceles: two sides are congruent
Classifying by its sides:
Scalene: no sides are congruent
Classifying by its angles:
Right: there is ONE right angle (90)
Obt
Chapter 4, Section 4
Proving Triangles are Congruent:
o ASA & AAS
o Angle-Side-Angle (ASA)
o Congruence Postulate
o If two angles and the included side of one triangle are congruent to two
angles and the included side of a second triangle , then the two t
Chapter 5, Section 1
Perpendiculars & Bisectors
Perpendicular Bisector
A segment, ray, line or plane which is perpendicular to a segment at its
midpoint is called a perpendicular bisector.
Equidistant
Same length (distance).
Perpendicular Bisector Theorem
Chapter 5, Section 3
Medians and Altitudes of a Triangle
Median of a Triangle
Is a segment whose endpoints are a vertex of the triangle & the midpoint
of the opposite side.
The point of concurrency of the medians is called the centroid of the
triangle.
Co