The area of Circle P is 16π. The area of Circle Q is 25π. The radius of Circle P is decreased by 50%. What is the new circumference of Circle P? (Use 3.14 for π)

12.56cm

Step-by-step explanation:

Step 1.

Find Radius of Circle P

Radius =

=

=4

Step 2.

Decrease by Radius by 50%

4×

=2

Step 3.

Find the new circumference using the new radius

C=πr²

=π×2²

=12.56

∴ The new circumference of Circle P is 12.56cm

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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.