Which of the following is not a theorem taught from this lesson? If two angles of a triangle are equal, then the sides opposite those angles are equal.
The altitude to the base of an isosceles triangle bisects the vertex angle of the triangle.
The base angles of an isosceles triangle are equal.
Corresponding Parts of Congruent Triangles are Congruent.

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?

Polygon abcde is reflected to produce polygon a′b′c′d′e′. what is the equation for the line of reflection?

Emily is entering a bicycle race for charity. her mother pledges $0.90 for every 0.75 mile she bikes. if emily bikes 18 miles, how much will her mother donate?