Complete the mapping of the vertices of DEF. y F
y + x

D(2, 4) - DU
E(1,-1) - E
D
F(5, 1) - F
F
E
X
-4
-2
What is the rule that describes a reflection across the
line y = x?
Tr=(x, y) -
E
2
-4
D

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 best explains why this triangle is or is not a right triangle?

What is the least common multiple for 6 and 8? what is the least common multiple for 4 and 12 ? what is the least common multiple for 11 and 12? what is the least common multiple for 3 and 6?