Title: Powerpoint Project 5
1Powerpoint Project 5
2Properties 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
3Equivalence 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
4Equivalence 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
5Overlapping 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
6Vertical 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)
7Congruence 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
8More 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
9Vocabulary 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
10Practice to Know and Love(and a pooton of it)
- Vertical Angles Definition, illustrated
examples, and an interactive practice quiz
11A 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_______
13Finding Values Problemas (To Know and Love)
3X- 60
120-6X
X40
10X