A sum of money is shared among Jen, Mary and Lilly in the ratio of 2:3:5. If Mary gives $27 to Jen, then both of them will have an equal amount of money. How much money does Lilly have?

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?

Which of the following correctly justifies statement four of the two column proof? a. corresponding angles theorem b. transitive property of equality c. vertical angle theorem d. substitution property of equality

Graph the equationy= x+3[tex]y = x + 3[/tex]