2.4 - Reasoning in Algebra and Geometry

2.4 - Reasoning in Algebra and Geometry

Operation Properties

• Addition, Subtraction, Multiplication, Division

• Must be done to both sides!

Properties of Equality

• Reflexive: x=x

• Symmetric: If x = y, then y = x.

• Transitive: If x = y and y = z, then x = z.

• Substitution: If a = b and 2b + 3 = x, then 2a + 3 =x.

Multiple Choice

What is the property of equality of the following:

If AB=CD, then CD=AB.

• Transitive

• Addition

• Multiplication

• Reflexive

• Symmetric

Multiple Choice

What is the property of equality of the following:

If m<A=50º, then 2m<A=100º

• Transitive

• Addition

• Multiplication

• Reflexive

• Symmetric

Multiple Choice

What is the property of equality of the following:

XY = XY

• Transitive

• Addition

• Multiplication

• Reflexive

• Symmetric

Multiple Choice

What is the property of equality of the following:

If m<A = m<B and m<B = m<C, then m<A = m<C.

• Transitive

• Addition

• Multiplication

• Reflexive

• Subtraction

Multiple Choice

What is the property of equality of the following:

If AB+CD=EF+CD, then AB=EF.

• Transitive

• Addition

• Multiplication

• Reflexive

• Subtraction

Multiple Choice

What is the property of equality of the following:

If m<5 = 30º, then m<5 + 5º = 35º.

• Transitive

• Addition

• Multiplication

• Reflexive

• Subtraction

Fill in the Blank

Use the property given to complete the statement.

Transitive Property:

If AE=CF and CF=EB, then _________.

Fill in the Blank

Use the property given to complete the statement.

Reflexive Property:

XY = ____

Fill in the Blank

Use the property given to complete the statement.

Multiplication Property:

If x=8, then 3x = ____.

Fill in the Blank

Use the property given to complete the statement.

Subtraction Property:

If AB + BC = DF + BC, then AB = ____.

Fill in the Blank

Use the property given to complete the statement.

Symmetric Property:

If AB = ZW, then _____.

Multiple Choice

Use the property given to complete the statement.

Transitive Property:
If

 $m\angle A=m\angle B\ \ and\ \ m\angle B=m\angle C$  , then ________ 

•  $m\angle A=m\angle C$  

•  $m\angle B=m\angle B$  

•  $m\angle A=m\angle A$  

Fill in the Blank

Use the property given to complete the statement.

Addition Property:

If x=15, then x+5= _______.

Fill in the Blank

Use the property given to complete the statement.

Reflexive Property:

If m<XYZ = _______.

Multiple Choice

Use the property given to complete the statement.

Symmetric Property:

If m<ABC = m<RST, then _______.

• $m\angle ABC=m\angle ABC$

• $m\angle RST=m\angle ABC$

• $m\angle RST=m\angle RST$
  

Multiple Choice

Use the property given to complete the statement.

Transitive Property:

If m<XYC = m<DEF, and m<DEF = m<RST then _______.

•  $m\angle XYC=m\angle XYC$ 

•  $m\angle XYC=m\angle RST$ 

•  $m\angle DEF=m\angle DEF$ 
  

Fill in the Blank

Use the property given to complete the statement.

Multiplication Property:

If AC = 17, then 3(AC) = _______.

Fill in the Blank

Use the property given to complete the statement.

Subtraction Property:

If AB = 42, then AB - 6 = _______.

Fill in the Blank

Use the property given to complete the statement.

Transitive Property:

If x=y and y=a, then _______.

Fill in the Blank

Use the property given to complete the statement.

Reflexive Property:

m<1= ________