Extended Response 12. For every metre a scuba diver dives below the water surface of a lake, the
light intensity is reduced by 5%. The percent of light intensity can be
represented by the equation I = 100(1.- 0.05), where I is the intensity of
light, as a percent, and d is the depth of the dive, in metres. The intensity
of light at the surface of the lake is 100%. Austin wanted to determine the
light intensity at a depth of 3 m. His solution is shown below.
I = 100(1 - 0.05)d
I = 100(1 - 0.05)3
I = 100(13 - 0.053)
I = 100(0.999875)
I 100
Austin realized that it is not possible for the light intensity to be
approximately 100% at a depth of 3 m. Explain where Austin made his
mistake.

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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.

c

step-by-step explanation: