Reasoning in Algebra

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

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 ________ 

• $$m\angle A=m\angle C$$  

• $$m\angle B=m\angle B$$  

• $$m\angle A=m\angle A$$  

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 _______.

• $$m\angle XYC=m\angle XYC$$

• $$m\angle XYC=m\angle RST$$

• $$m\angle DEF=m\angle DEF$$