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Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ∠dab = x, and ∠abc = 90◦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ∠pad = ∠pbc. but pab is isosceles, hence ∠pab = ∠pba. subtracting, gives x = ∠pad−∠pab = ∠pbc −∠pba = 90◦. this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?

What is the length of the unknown leg in the right triangle ?

A. the following events are mutually exclusive: living in california and watching american idol. true or false b. the number of patients seen by an outpatient practice is an example of a discrete random variable. true or false c.the law of large numbers states that as the number of times an event experiment is conducted increases, the likelihood of the actual probability of an event approaching the theoretical probability decreases. true or false d. measuring the time it takes for patients to enter the operating room is an example of a continuous random variable. true or false