TEST DUE TOMORROW PLEASE HELP I WILL GIVE YOU BRAINLIEST what information is necessary to prove the triangles congruent by SSS and by HL? show work pls

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?

Issof claims that the scale factor is 1/2. which statement about his claim is correct

Given that ot =5, xt=12, and ox= 13 is xy tangent to circle o at t? explain.