Given: In triangle ABC, ∠B ≅ ∠C Prove: AB ≅ ACTriangle A B C is shown. Angles A B C and B C A are congruent. Complete the paragraph proof. We are given that ∠B ≅ ∠C. Assume segment AB is not congruent to . If AB > AC, then m∠C > m∠B by the . If AB < AC, then m∠C < m∠B by the converse of the triangle parts relationship theorem. But by the definition of congruent, we know the measure of angle B equals the measure of by the given statement. Therefore, we have a contradiction: AB = AC, and AB ≅ AC.

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.