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Powerpoint Project 5

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Powerpoint Project 5 Adam and Nikki Birnbrey Properties of Equality to Know and Love Addition Property- If a=b, then a+c= b+c Subtraction Property- If a=b, then a-c=b ... – PowerPoint PPT presentation

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Title: Powerpoint Project 5


1
Powerpoint Project 5
  • Adam and Nikki
  • Birnbrey

2
Properties of Equality to Know and Love
  • Addition Property- If ab, then ac bc
  • Subtraction Property- If ab, then a-cb-c
  • Multiplication Property- If ab, then acbc
  • Division Property- If ab and c doesnt 0
  • Then a/c b/c
  • Substitution Property- If ab you may replace a
    with b in any equation containing a in the result

3
Equivalence Properties of Equality to Know and
Love
  • Reflexive Property- For any real number a, aa
  • Symmetric Property- For all real numbers a and b,
    if ab, then ba
  • Transitive Property- For all real numbers a, b,
    and c, if ab and bc, then ac

4
Equivalence Relation To Know And Love any
relation that satisfies these equivalence
properties
  • Reflexive Property- Figure AFigure A
  • A
  • Symmetric Property- If Figure AFigure B, then
    Figure BFigure A
  • A
  • Transitive Property- If Figure AFigure B and
    Figure BFigure C, Then Figure AFigure C
  • A B C

5
Overlapping Theorem to Know and Love
  • Overlapping Segments- Given a segment with points
    A, B, C, D arranged as shown the following
    statements are true
  • 1. If ABCD then ACBD
  • 2. If ACBD then ABCD
  • Overlapping Angles- Given Angle AED with points B
    and C in its interior as shown, the following
    statements are true
  • 1. If Angle AEBAngle CED then ?
  • 2. If Angle AECAngle BED then ?

A B C D
A
B
C
D
E
6
Vertical Angles Theorem to Know and Love
  • If two angles form a pair of vertical angles,
    then they are congruent.
  • Given angle 1 and 2 are vertical angles
  • Prove Angle 1 and 2 are congruent
  • Statements
    Reasons

4
1
2
3
Given Linear pair property Substitution
property of equality Subtraction property of
equality
  • Angle 1 and 2 are vertical angles
  • 2. Angle 1 angle 2 180
  • Angle 2 angle 3 180
  • 3. Angle 1 angle 3 angle 2 angle 3
  • 4. Angle 1 angle 2 (12)

7
Congruence Supplements Theorem to Know and Love
  • If two angles are supplements of congruent angles
    then the two angles are congruent
  • Given Angle 1Angle 3, Angle 1 and angle 2 are
    supplementary, Angle 3 and 4 are supplementary
  • Prove Angle 2Angle 4
  • Statements Reasons

3
4
1
2
1. lt1lt2180 lt3lt4180 2. lt1lt2lt3lt4 3.
lt1lt3 4. lt1lt2lt1lt4 5. lt2lt4
Definition of Supplementary Angles Transitive Giv
en Substitution Property Subtraction Property
8
More Theorems to Know and Love
  • Theorem- Reflection across two parallel lines is
    equivalent to a translation of twice the distance
    between the lines and in a direction
    perpendicular to the lines
  • Theorem- Reflection across two intersecting lines
    is equivalent to a rotation about the point of
    intersection through twice the measure of the
    angle between the lines

9
Vocabulary to Know and Love
  • Equivalence relation Any relation that satisfies
    the Reflexive, Symmetric, and Transitive
    Properties
  • Inductive reasoning The process of forming
    conjectures that are based on observations
  • Paragraph proof A form of a proof in which ones
    reasoning is explained in paragraph form, as
    opposed to a two-column proof
  • Theorem A statement that has been proved
    deductively
  • Two column proof A proof in which the statements
    are written in the left-hand column and the
    reasons are given in the right-hand column
  • Vertical angles The opposite angles formed by
    two intersecting lines

10
Practice to Know and Love(and a pooton of it)
  • Vertical Angles Definition, illustrated
    examples, and an interactive practice quiz

11
A real pooton of Practice to Know and Love (yeah
math?)
  • Given 15x-510x15
  • (use properties to prove)
  • Prove the Overlapping Segments Theorem
  • Given WXYZ Prove WYXZ

W X Y Z
segment additon postulate ______pr
operty
WXYZ WXXY YZXY WXXYWY
12
.Extra poo
  • Identify the properties of equality that justify
    the conclusion.
  • ltB ltC ltC ltD? ltB ltD ________
  • ABCD CDAB_______
  • ABBC BC CD ACBD_______

13
Finding Values Problemas (To Know and Love)
  • Find x.

3X- 60
120-6X
X40
10X
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