A5 foot woman stands near a 4 foot cello case. the cello case casts a shadow that is 6 ft long. how long is the shadow cast by the woman? your

Her shadow is 7.5 feet

Step-by-step explanation:

The ratios are the same so

Cello case height                cello shadow

 =      

  woman height                   woman shadow

 4          6

__   =  ___    cross multiply

  5          x

4(x) = 6(5)

4x  =  30

/4       /4

 x = 7.5

∠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: 4 cause 2+2=4