Download - Friday, September 13 th
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Friday, September 13th
1. Z is the centroid. If Line 2. XZ = 5. Find XLZK= 10 Find the median KW
Warm Up
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QuizAnswers
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Part 1: Centroid
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1. Vertex to centroid=2/3 the distance of the median
2. Midsegment to centroid = 1/3 the distance of the median
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Part 2: Circumcenter
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1. All Vertexes to circumcenter are EQUAL2. All corresponding sides are equal
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HomeworkAnswers
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PROOFS
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On a sheet of paper, write down how you
would make a peanut butter and jelly
sandwich
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When we write proofs, we have to write every step!!!
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Part IAlgebraic
Proofs
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Subtraction Property of Equality
Subtracting the same number to both sides of an equation does not change
the equality of the equation.If a = b, then a – c = b – c.Ex: x = y, so x – 4 = y – 4
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Addition Property of Equality
Adding the same number to both sides of an equation
does not change the equality of the equation.
If a = b, then a + c = b + c.Ex: x = y, so x + 4 = y +4
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Multiplication Property of Equality
Multiplying both sides of the equation by the same number, other than 0, does not change the equality of the equation.If a = b, then ac = bc.Ex: x = y, so 3x = 3y
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Division Property of Equality
Dividing both sides of the equation by the same
number, other than 0, does not change the equality of
the equation.If a = b, then a/c = b/c.Ex: x = y, so x/7 = y/7
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Commutative PropertyChanging the order of addition
or multiplication does not matter.
“Commutative” comes from “commute” or “move around”, so the Commutative Property is the one that refers to moving
stuff around.
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Commutative Property
Addition: a + b = b + a
Ex: 1 + 9 = 9 + 1
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Commutative Property
Multiplication: a ∙ b = b ∙ a
Ex: 8 ∙ 6 = 6 ∙ 8
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Associative Property
The change in grouping of three or more terms/factors does not change their sum or product.
“Associative” comes from “associate” or “group”, so the Associative Property is the one
that refers to grouping.
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Associative Property
◦Addition: a + (b + c) = (a + b) + c
Ex: 1 + (7 + 9) = (1 + 7) + 9
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Associative Property
Multiplication: a ∙ (b ∙ c) = (a ∙ b) ∙ c
Ex: 8 ∙ (3 ∙ 6) = (8 ∙ 3) ∙ 6
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Distributive Property
The product of a number and a sum is equal to the sum of
the individual products of terms.
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Distributive Property
a ∙ (b + c) = a ∙ b + a ∙ c
Ex: 5 ∙ (x + 6) = 5 ∙ x + 5 ∙ 6
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Reflexive PropertyThink: Mirror
A= A
-3 = -3M<1= m<1
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Symmetric PropertyIf a = b then b = a
-3 = x then X= - 3
If xy is vw then vw is xy
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Transitive PropertyFor any numbers a, b, and c, if a = b and b = c, then a = c
If < 1 <2, and <2 <3 then <1 <3
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The Distributive Property states that a(b + c) = ab + ac.
Remember!
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Solve the equation 4m – 8 = –12. Write a justification for each step.
4m – 8 = –12 Given equation +8 +8 Addition Property of Equality 4m = –4 Simplify.
m = –1 Simplify.
Division Property of Equality
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t = –14 Simplify.
Solve the equation . Write a justification for each step.
Given equation
Multiplication Property of Equality.
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Identify the property that justifies each statement.A. QRS QRS B. m1 = m2 so m2 = m1 C. AB CD and CD EF, so AB EF.D. 32° = 32°
Identifying Property of Equality and Congruence
Symm. Prop. of =
Trans. Prop of
Reflex. Prop. of =
Reflex. Prop. of .
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ReviewSolve each equation. Write a justification for each step.
1.
z – 5 = –12 Mult. Prop. of =z = –7 Add. Prop. of =
Given
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Solve each equation. Write a justification for each step.
2. 6r – 3 = –2(r + 1)
Given6r – 3 = –2r – 28r – 3 = –2
Distrib. Prop.Add. Prop. of =
6r – 3 = –2(r + 1)
8r = 1 Add. Prop. of =Div. Prop. of =
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Identify the property that justifies each statement.
3. x = y and y = z, so x = z.
4. DEF DEF
5. AB CD, so CD AB.
Trans. Prop. of =
Reflex. Prop. of Sym. Prop. of