Question

which property is illustrated?
if \\( \angle a \cong \angle b \\), then \\( \angle b \cong \angle a \\)
associative property of angles
reflexive property of congruence
transitive property of congruence
symmetric property of congruence

1. choose the best answer.

which property is illustrated?
\\( x + y = y + x \\)
commutative property of addition
symmetric property of addition
reflexive property of equality
symmetric property of equality

Explanation:

First Question

• Associative Property of Angles: Deals with grouping of angles, not relevant here.
• Reflexive Property of Congruence: States \( \angle A\cong\angle A\), not the case here.
• Transitive Property of Congruence: If \( \angle A\cong\angle B\) and \( \angle B\cong\angle C\), then \( \angle A\cong\angle C\), not applicable.
• Symmetric Property of Congruence: If \( \angle A\cong\angle B\), then \( \angle B\cong\angle A\), which matches the given statement.

• Commutative Property of Addition: States \(a + b=b + a\), which matches \(x + y=y + x\).
• Symmetric Property of Addition: Not a standard property name in basic arithmetic (commutative is the correct term for \(a + b=b + a\)).
• Reflexive Property of Equality: States \(a=a\), not relevant.
• Symmetric Property of Equality: States if \(a = b\), then \(b=a\), but the given is about the order of addition (commutative for addition operation).

Answer:

Symmetric Property of Congruence

Second Question