Practice Page
Directions: Prepare a coordinate geometry proof for each problem. Some problems specify a method, while others leave the choice of method up to you. While more than one method of proof, or presentation, is possible, only one possible answer will be shown for each question.

1.
Given: quadrilateral PQRS with
P(-4,-2), Q(-2,3), R(4,3) and
S(2,-2).

Prove: PQRS is a parallelogram using slopes.



proof3


 

 

2.
Given: ΔDOG with D(-2,5), O(-4,1) and G(-10,4)

Show: ΔDOG is a right triangle


dogtriangle

 



3.
Given: quadrilateral FRED with
F(0,3), R(4,5), E(5,3) and D(1,1)

Prove: FRED is a rectangle

 


fredchair

 



4.
Given: quadrilateral ABCD with
A
(5,1), B(0,3), C(-2,5) and D(3,3)

Show: ABCD is a parallelogram
using midpoints.




surfer



 

5.
Given: quadrilateral CDEF with
C(-2,3), D(-5,-4), E(2,-1) and
F(5,6)

Prove: CDEF is a rhombus but not a square


chairguy

 



6.
Given: ΔFUN with F(4,-1), U(5,6) and N(1,3)

Show: ΔFUN is an isosceles right triangle


trilips



 

7.
Given: quadrilateral TRAP with
T(-5,7), R(-3,-4), A(9,5) and P(-1,10)

Show: TRAP is an isosceles trapezoid

 

trappen

 



8.
Given: quadrilateral ARMY with
A(p,q), R(0,0), M(r,0) and Y(p+r,q)

Prove ARMY is a parallelogram.


armypic

 



9.
Given: ΔPQR with P(-1,4), Q(3,0),
and R(-2,-3)

Prove ΔPQR is NOT a right triangle.


showans9

 



10.
Given: Circle O with center at
(-1,1) and point G(2,-3) lies on the circle.

Create a proof to show whether point Q(3,3) lies on the circle, or not.


showans10


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