This model of the backboard of a basketball goal is composed of a rectangle and a semicircle. Use a ruler to measure the dimensions of the model to the nearest half inch. Which measurement is closest to the area of the model of the backboard in square inches?

12inches

Step-by-step explanation:

Area of the backboard = Area of the rectangle+area of the semicircle

Area of a rectangle = Length × Width

Area of the semicircle = πd²/8

Area of the backboard = LW+πd²/8

From the diagram, we are given

L = 1.5inches

W = 4inches = diameter of the semicircle

Substitute the given parameters into the formula:

Area of the backboard = (1.5×4)+(π(4)²/8)

Area of the backboard = 6.0+16(3.14)/8

Area of the backboard = 6.0+2(3.14)

Area of the backboard = 6.0+6.28

area of the backboard = 12.28in²

Hence the measurement closest to the area of the model of the backboard in square inches is 12inches

∠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.