Please help, i’ve been trying to do it, i don’t get it tho

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?

Given the diagram below, michael writes, "segment ac is congruent to segment ac." which of the following reasons allow him to write this statement?

The data set represents the ages of players in a chess club. 27, 34, 38, 16, 22, 45, 54, 60. what is the mean absolute deviation of the data set?