Which property justifies the following statement? if ∠a ≅ ∠b, and ∠b ≅ ∠c, then ∠a ≅ ∠c. transitive property of congruence reflexive property of congruence distributive property symmetric property of congruence

Transitive property of congruence.

Step-by-step explanation:

The transitive property of congruence states that if ∠A≅∠B, ∠B≅∠C then ∠A≅∠C.

For example:

x+5= 10 and 10= 5+5 then x+5= 5+5.

Transitive property of congruence.

Step-by-step explanation:

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<Jayla>

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

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step-by-step explanation: