Please prove the following theorems:

If two arcs of a circle are congruent, then the corresponding chords are congruent.

How to determine whether two known pairs of points are on the same line.

Atextile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. the company wishes to test the hypothesis upper h subscript 0 baseline colon mu equals 12 against upper h subscript 1 baseline colon mu less-than 12 using a random sample of n equals 4 specimens. calculate the p-value if the observed statistic is x overbar equals 11.8. round your final answer to five decimal places (e.g. 98.76543).

Which word in the sentence below is an interrogative pronoun? who is picking us up from school? whousisfrom