() the congruency of mno and xyz can be proven using a reflection across the line bisecting oz. however, this congruency can also be proven using geometric postulates, theorems, and definitions. prove that the triangles are congruent using a two-column proof and triangle congruency theorems.

Arandom sample of n = 25 observations is taken from a n(µ, σ ) population. a 95% confidence interval for µ was calculated to be (42.16, 57.84). the researcher feels that this interval is too wide. you want to reduce the interval to a width at most 12 units. a) for a confidence level of 95%, calculate the smallest sample size needed. b) for a sample size fixed at n = 25, calculate the largest confidence level 100(1 − α)% needed.