Question

which property of congruence is illustrated? for any geometric figures a, b, and c, if a ≅ b and b ≅ c, then a ≅ c.
reflexive
symmetric
transitive
commutative

1. choose the best answer.

which property of congruence is illustrated?
for any geometric figures a and b, if a ≅ b, then b ≅ a.
reflexive
transitive
commutative

Explanation:

First Question (Top One)

• Reflexive property: A ≅ A (a figure is congruent to itself), which doesn't match the given statement.
• Symmetric property: If A ≅ B, then B ≅ A (reverse order), not the transitive - like chain here.
• Transitive property: If A is related to B and B is related to C, then A is related to C. The statement "if A ≅ B and B ≅ C, then A ≅ C" fits this transitive structure for congruence.
• Commutative property is more about operations (like addition: a + b = b + a) and not a congruence property in this context.

• Reflexive property: A ≅ A, which is not what's shown here.
• Transitive property: Involves three figures (A, B, C) with a chain of congruence, but this question has two figures (A, B) and a reverse of congruence.
• Commutative property is for operations, not congruence relations in this way.
• Symmetric property: If A ≅ B, then B ≅ A. The statement "if A ≅ B, then B ≅ A" matches the symmetric property of congruence. (Note: There might be a typo in the original options as "Symmetric" should be an option here, maybe it was cut off. Assuming "Symmetric" is the intended correct option among the standard congruence properties, as the given options seem to have a formatting issue but the logic is about reversing the congruence relation between two figures.)

Answer:

C. Transitive

Second Question (Bottom One)