If a series of rigid transformations maps ∠F onto ∠C where ∠F is congruent to ∠C, then which of the following statements is true?

triangles ABC and FDE, in which angles A and D are right angles

ΔABC ~ ΔDEF because of the definition of similarity in terms of similarity transformations
segment BC ~ segment DE because of the AA similarity postulate
ΔABC ~ ΔDEF because of the AA similarity postulate
segment BC ~ segment DE because of the definition of similarity in terms of similarity transformations

In a sample of 2023 u.s. adults, 373 said franklin roosevelt was the best president since world war ii. two u.s. adults are selected at random from the population of all u.s. adults without replacement. assuming the sample is representative of all u.s. adults, complete parts (a) through (d). (a) find the probability that both adults say franklin roosevelt was the best president since world war ii. the probability that both adults say franklin roosevelt was the best president since world war ii is (round to three decimal places as needed.) (b) find the probability that neither adult says franklin roosevelt was the best president since world war ii. the probability that neither adult says franklin roosevelt was the best president since world war ii is (round to three decimal places as needed.) (c) find the probability that at least one of the two adults says franklin roosevelt was the best president since world war ii. the probability that at least one of the two adults says franklin roosevelt was the best president since world war ii is (round to three decimal places as needed.) (d) which of the events can be considered unusual? explain. select all that apply. the event in part left parenthesis a right parenthesis is unusual because its probability is less than or equal to 0.05. the event in part (b) is unusual because its probability is less than or equal to 0.05. none of these events are unusual. the event in part (c) is unusual because its probability is less than or equal to 0.05.

What is the missing step in this proof ?

Does the point (1, sqrt 7) lie on circle shown.