coordinate proofs

Question 1

how do i prove a quad is a trapezoid?

Answer 1

1 pair of parallel sides
(slope 2x)

Question 2

how do i prove a quad is an isosceles trapezoid

Answer 2

1 pair parallel sides and 1 pair congruent legs
(slope and distance 2x)

Question 3

how do i prove a quad is a parallelogram

Answer 3

-2 pairs of opposite sides parallel sides (slope 2x)
-2 pairs of opposite sides are congruent (distance 2x)
-2 pair of opposite sides both parallel and congruent (slope 2x, distance 2x)
Diagonals bisect each other (Use midpoint formula)

Question 4

how do i prove a quad is a rectangle?

Answer 4

1) prove that its a parallelogram first (choose one method)
ex: 2 pairs of opposite sides

2) prove that it is a rectangle