Exploring Two-Column Proofs in Algebra

What is the main focus of the new unit introduced in the video?

• Angles and lines

• Calculus

• Trigonometry

• Algebraic equations

Which property states that if a = b, then a + c = b + c?

• Subtraction Property

• Multiplication Property

• Addition Property

• Division Property

What must be true for the Division Property of Equality to hold?

• c must not be zero

• a must be greater than b

• b must be greater than c

• a must equal b

Which property states that a number is always equal to itself?

• Symmetric Property

• Transitive Property

• Reflexive Property

• Substitution Property

If a = b and b = c, which property allows us to conclude that a = c?

• Substitution Property

• Symmetric Property

• Transitive Property

• Reflexive Property

What is the purpose of a two-column proof?

• To list statements and reasons in an organized manner

• To simplify complex equations

• To solve equations faster

• To avoid using algebraic properties

In the example proof, what property justifies combining like terms?

• Addition Property

• Simplifying

• Division Property

• Subtraction Property

What is the final step in solving the algebraic proof example?

• Combining like terms

• Using the symmetric property

• Using the addition property

• Using the division property

In the geometric proof example, what property is used to show that AC = AB + BC?

• Segment Addition Postulate

• Substitution Property

• Transitive Property

• Symmetric Property

Why is the substitution property used in the geometric proof example?

• To combine like terms

• To replace equal segments with their equivalents

• To add the same value to both sides

• To divide both sides by the same value