Prove NOT
Diagonals and Trapezoids
Mixed Bag

What is the slope formula?

m = (y2-y1)/(x2-x1)


Quadrilateral PQRS has vertices P(−2, 3), Q(3, 8), R(4, 1), and S(−1, −4). Prove that PQRS is not a square.

Because the slopes of adjacent sides are not opposite reciprocals, they are not perpendicular and do not form a right angle. Therefore PQRS is not a square.


In rhombus MATH, the coordinates of the endpoints of the diagonal MT are M(0,−1) and T(4,6). Write an equation of the line that contains diagonal AH.

y − 2.5 = −4 7 (x − 2) The diagonals, MT and AH, of rhombus MATH are perpendicular bisectors of each other


Quadrilateral KATE has vertices K(1, 5), A(4, 7), T(7, 3), and E(1, −1). Prove that KATE is a trapezoid.

To prove that KATE is a trapezoid, show that one pair of opposite sides of the figure are parallel by showing that they have the same slope and that the other pair of opposite sides is not parallel by showing they do not have the same slope.


Machu Picchu is located in Peru, Uruguay, or Columbia?



What is the midpoint formula?

M = (x2+x1/2 , y2+y1/2)


The vertices of quadrilateral JKLM have coordinates J(−3, 1), K(1, −5), L(7, −2), and M(3, 4). Prove that JKLM is a parallelogram. Prove that JKLM is not a rhombus.

Since both opposite sides have equal slopes and are parallel, JKLM is a parallelogram.

JM is not congruent to ML, so JKLM is not a rhombus since not all sides are congruent.


Find the coordinates of the intersection of the diagonals of quadrilateral ABCD with vertices A(1, 3), B(6, 2), C(4, -2), and D(-1, -1)

(2.5, .5)


In the coordinate plane, the vertices of RST are R(6, −1), S(1, −4), and T(−5, 6). Prove that RST is a right triangle. 

Since the slopes of TS and SR are opposite reciprocals, they are perpendicular and form a right angle. RST is a right triangle because ∠S is a right angle. 


The capital of Connecticut is New Haven, Boston, or Hartford?



What is the distance formula?



Quadrilateral MATH has coordinates M(1,1), A(−2,5), T(3,5), and H(6,1). Prove that quadrilateral MATH is a rhombus, and prove that it is not a square.

The length of each side of quadrilateral is 5. Since each side is congruent, quadrilateral MATH is a rhombus. The slope of MH is 0 and the slope of HT is -4/3 . Since the slopes are not negative reciprocals, the sides are not perpendicular and do not form rights angles. Since adjacent sides are not perpendicular, quadrilateral MATH is not a square.


Prove that quadrilateral MILK with the vertices M(1,3), I(-1,1), L(-1, -2), and K(4,3) is an isosceles trapezoid.

Prove 2 sides parallel

Prove 2 sides congruent but not parallel


In the coordinate plane, the vertices of triangle PAT are P(−1, −6), A(−4, 5), and T(5, −2). Prove that PAT is an isosceles triangle.

PAT is an isosceles triangle because sides AP and AT are congruent.


What was the first ice cream flavor by Ben and Jerry's? Vanilla, chocolate, or strawberry


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