1. cot sec θ θ 2. θ θ cot csc 3. θθ ∙ θθ θθ 4. θ − θ 2 2 cos 1 cos 5. cos tan θ θ 6. θ θ csc sec 7. 2θθ − 2θθ2θθ 8. θ θ ( + ) 2 cos 1 tan Verify the trig identity 9. θθ θθ θθ = θθ 10. θθ + θθ 22θθ = θθ 11. θθ θθ + θθ θθ = 11 12. 22θθ− θθ θθ = θθ − θθ

∠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.

step-by-step explanation:

options

step-by-step explanation: s