8. In the figure, a circle is inscribed in a square
ABCD. If the area of the square is 81 cm², find
the area of the circle.
(Give the answer correct to 3 significant figures.)

63.6cm²

Step-by-step explanation:

Area of square = 81

Side of square =

                        = 9

-----------------------------------------

diameter of circle = 9

radius of circle = 9 ÷ 2

                        = 4.5

area of circle = πr²

                      = π (4.5)²

                      = 63.6172512  

                      ≈ 63.6 cm²

∠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.