Which ratio forms a proportion 12/15

Step-by-step explanation:

See Attachment for Complete Question

Given

Required

Determine its equivalent proportion

Factorize the given expression

Divide the numerator and denominator by 3

We apply the same steps to the given options as follows:

1.

Factorize

Divide the numerator and denominator by 7

This is not an equivalent proportion of

2.

Factorize

Divide the numerator and denominator by 5

This is equivalent to because they both simplify to

There's no need to check the last option;

Hence, the option that answers the question is

∠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.

answer: 2530

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