Define a relation Q on the set Rx R as follows. For all ordered pairs (w, x) and (y, z) in RxR, (w, x) Q (y, z) = x= z. (a) Prove that is an equivalence relation. To prove that is an equivalence relation, it is necessary to show that is reflexive, symmetric, and transitive. Proof that Q is an equivalence relation: (1) Proof that Q is reflexive: Construct a proof by selecting sentences from the following scrambled list and putting them in the correct order.
a. By the reflexive property of equality, x = x
b. By definition of Q, (w, x) = (w, x).
c. By the symmetric property of equality, w = w.
d. By the reflexive property of equality, w = w.
e. By the symmetric property of equality, x = x.

there is no picture

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∠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.

greater than one

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