Question

for all expressions a, b, and c, if a = b, then a + c = b + c.
○ commutative property of addition
○ distributive property of equality
○ addition property of equality
○ associative property of addition

1. choose the best answer.

which property of congruence is illustrated?
for any geometric figure a, a ≅ a.
○ transitive
○ symmetric
○ commutative
○ reflexive

Explanation:

First Question (About Equality Property)

• Commutative Property of Addition: States \(a + b = b + a\), not about adding to both sides of an equality.
• Distributive Property of Equality: Not a standard property; distributive is \(a(b + c)=ab + ac\), not for equality with addition.
• Addition Property of Equality: Defined as if \(a = b\), then \(a + c = b + c\), which matches the given statement.
• Associative Property of Addition: States \((a + b)+c = a+(b + c)\), about grouping, not adding to both sides.

• Transitive Property of Congruence: If \(A\cong B\) and \(B\cong C\), then \(A\cong C\), not about a figure congruent to itself.
• Symmetric Property of Congruence: If \(A\cong B\), then \(B\cong A\), about reversing the congruence.
• Commutative Property: Not a congruence property (commutativity is for operations like addition/multiplication).
• Reflexive Property of Congruence: States any geometric figure is congruent to itself (\(A\cong A\)), which matches the given statement.

Answer:

C. Addition Property of Equality

Second Question (About Congruence Property)