Powerpoint Project 5

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Powerpoint Project 5

• Adam and Nikki
• Birnbrey

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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

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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

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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

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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
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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

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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)

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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

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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
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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

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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

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Practice to Know and Love(and a pooton of it)

• Vertical Angles Definition, illustrated
  examples, and an interactive practice quiz

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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
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.Extra poo

• Identify the properties of equality that justify
  the conclusion.
• ltB ltC ltC ltD? ltB ltD ________
• ABCD CDAB_______
• ABBC BC CD ACBD_______

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Finding Values Problemas (To Know and Love)

• Find x.

3X- 60
120-6X
X40
10X