What is the circumference of the following figure? be sure to convert your answer to yards.
a-56.52yd
b-1.57yd
c-4.71yd
d-28.26yd

The circumference of the given circular figure is 1.57 yards.

Step-by-step explanation:

Here, the diameter of the given figure is 18 inches.

Now, Diameter = 2 x Radius

Radius =  d/2 = 18 / 2 = 9 inches

⇒ R = 9 inches

Now, Circumference of the Circle = 2πr

or, Circumference = 2 x 3.14 x 9

                              =  56.52 inches

Now, 1 inch =  0.02777 yard

⇒ 56.52 inches = (0.02777  x 56.52  ) yard

                           = 1.57 yard

Hence, the circumference of the given circular figure is 1.57 yards.

∠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.

can someone me: the midsegment through the legs of an isosceles triangle is 4 in. find the sides of the triangle if its perimeter is 20 in. ,   and point g is the centroid of the right △abc with hypotenuse ab=18 in. find cg.