Groundhog's day is on february 2nd each year. on this day, in punxsatawney, pennsylvania, thousands of onlookers watch to see if phil, the groundhog, will cast a shadow. if he does, then six more weeks of winter are predicted. if he doesn't, then an early spring is predicted. historically, phil's prediction has only been correct about 40% of the time. using complete sentences, design a simulation to determine the probability that phil's prediction will be correct at least two out of the next three years. make sure to explain how you would use the simulation to determine the probability.

∠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.

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step-by-step explanation:

a

step-by-step explanation: