Question

willhite_k. geometry a_section 1_fall 25/26 / unit 2 - logic and proofs which property is illustrated? ∠a ≅ ∠a symmetric property of congruence transitive property of congruence reflexive property of congruence reflexive property of angles 21. choose the best answer. which property is illustrated? (3x)y = 3(xy) commutative property of multiplication distributive property of equality associative property of multiplication

Explanation:

First Question (∠A ≅ ∠A)

• The Reflexive Property of Congruence states that any geometric figure (like an angle, segment, etc.) is congruent to itself. Here, ∠A is congruent to ∠A, which matches this property.
• The Symmetric Property is if \( a \cong b \), then \( b \cong a \), which is not the case here.
• The Transitive Property is if \( a \cong b \) and \( b \cong c \), then \( a \cong c \), which also doesn't apply.
• "Reflexive Property of Angles" is not a standard congruence property term; the correct term is Reflexive Property of Congruence.

• The Associative Property of Multiplication states that the way we group factors in a multiplication operation does not change the product, i.e., \( (ab)c = a(bc) \). Here, \( (3x)y = 3(xy) \) shows the grouping of \( 3 \) and \( x \) (or \( x \) and \( y \)) is changed, but the product remains the same, so it's the Associative Property of Multiplication.
• The Commutative Property is about the order of factors (\( ab = ba \)), which is not shown here.
• The Distributive Property involves multiplying a sum by a number (\( a(b + c)=ab + ac \)), which is not the case here.

Answer:

C. Reflexive Property of Congruence

Second Question ((3x)y = 3(xy))