Exploring Algebraic and Geometric Proofs

What is the Addition Property of Equality?

• If a = b, then a + c = b + c

• If a = b, then a - c = b - c

• If a = b, then a/c = b/c

• If a = b, then ac = bc

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

• Reflexive Property

• Substitution Property

• Symmetric Property

• Transitive Property

What is the Transitive Property?

• If a = b, then a - c = b - c

• If a = b, then a + c = b + c

• If a = b and b = c, then a = c

• If a = b, then ac = bc

What is the first step in any two-column proof?

• State the given information

• Combine like terms

• Solve the equation

• Use the transitive property

In a two-column proof, what is the reason for the first statement?

• Subtraction Property of Equality

• Symmetric Property

• Given

• Addition Property of Equality

What property allows you to flip the order of an equation?

• Reflexive Property

• Transitive Property

• Substitution Property

• Symmetric Property

What is the Substitution Property?

• If a = b, then ac = bc

• If a = b, then a - c = b - c

• Replacing a value with another equal value in an equation

• If a = b, then a + c = b + c

What is the final step in solving the equation 3x - 4 = 4x + 2?

• Divide both sides by 5

• Use the symmetric property to flip the equation

• Add 4 to both sides

• Subtract 3x from both sides

What is the definition of congruent angles?

• Angles that are adjacent

• Angles that are complementary

• Angles that are supplementary

• Angles that have the same measure

What is the measure of angle ABC if it is given as 3x - 5 and x = 27?

• 81

• 76

• 100

• 90