Friday, September 13th

1. Z is the centroid. If Line 2. XZ = 5. Find XLZK= 10 Find the median KW

Warm Up

QuizAnswers

Part 1: Centroid

1. Vertex to centroid=2/3 the distance of the median

2. Midsegment to centroid = 1/3 the distance of the median

Part 2: Circumcenter

1. All Vertexes to circumcenter are EQUAL2. All corresponding sides are equal

HomeworkAnswers

PROOFS

On a sheet of paper, write down how you

would make a peanut butter and jelly

sandwich

When we write proofs, we have to write every step!!!

Part IAlgebraic

Proofs

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

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

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

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

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.

Commutative Property

Addition: a + b = b + a

Ex: 1 + 9 = 9 + 1

Commutative Property

Multiplication: a ∙ b = b ∙ a

Ex: 8 ∙ 6 = 6 ∙ 8

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.

Associative Property

◦Addition: a + (b + c) = (a + b) + c

Ex: 1 + (7 + 9) = (1 + 7) + 9

Associative Property

Multiplication: a ∙ (b ∙ c) = (a ∙ b) ∙ c

Ex: 8 ∙ (3 ∙ 6) = (8 ∙ 3) ∙ 6

Distributive Property

The product of a number and a sum is equal to the sum of

the individual products of terms.

Distributive Property

a ∙ (b + c) = a ∙ b + a ∙ c

Ex: 5 ∙ (x + 6) = 5 ∙ x + 5 ∙ 6

Reflexive PropertyThink: Mirror

A= A

-3 = -3M<1= m<1

Symmetric PropertyIf a = b then b = a

-3 = x then X= - 3

If xy is vw then vw is xy

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

The Distributive Property states that a(b + c) = ab + ac.

Remember!

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

t = –14 Simplify.

Solve the equation . Write a justification for each step.

Given equation

Multiplication Property of Equality.

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 .

ReviewSolve each equation. Write a justification for each step.

1.

z – 5 = –12 Mult. Prop. of =z = –7 Add. Prop. of =

Given

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 =

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