SOLUTION: Given: E(-2,3) F(-2,-2) G(3,-2) H(3,3) Prove: EFGH is a rhombus

Algebra ->  Geometry-proofs -> SOLUTION: Given: E(-2,3) F(-2,-2) G(3,-2) H(3,3) Prove: EFGH is a rhombus       Log On


   

Question 1125238: Given: E(-2,3) F(-2,-2) G(3,-2) H(3,3)
Prove: EFGH is a rhombus
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Ways to prove that a quadrilateral is a rhombus:
Show that it has four congruent sides. ( by definition of rhombus)
Given:
E(-2,3)
F(-2,-2)
G(3,-2)
H(3,3)
Prove: EFGH is a rhombus
find distance between two points:EF, FG,GH, and EH
E(-2,3)
F(-2,-2)
EF=sqrt%28%28x-x%5B1%5D%29%5E2%2B%28y-y%5B1%5D%29%5E2%29
EF=sqrt%28%28-2%29-%28-2%29%29%5E2%2B%283-%28-2%29%29%5E2%29
EF=sqrt%28%28-2%2B2%29%5E2%2B%283%2B2%29%5E2%29
EF=sqrt%280%5E2%2B5%5E2%29
highlight%28EF=5%29
F(-2,-2)
G(3,-2)
FG=sqrt%28%28x-x%5B1%5D%29%5E2%2B%28y-y%5B1%5D%29%5E2%29
FG=sqrt%28%283-%28-2%29%29%5E2%2B%28-2-%28-2%29%29%5E2%29
FG=sqrt%28%283%2B2%29%5E2%2B%28-2%2B2%29%5E2%29
FG=sqrt%285%5E2%2B0%5E2%29
FG=sqrt%285%5E2%29
highlight%28FG=5%29
G(3,-2)
H(3,3)
GH=sqrt%28%28x-x%5B1%5D%29%5E2%2B%28y-y%5B1%5D%29%5E2%29
GH=sqrt%28%283-3%29%5E2%2B%283-%28-2%29%29%5E2%29
GH=sqrt%280%5E2%2B%283%2B2%29%5E2%29
GH=sqrt%285%5E2%29
highlight%28GH=5%29

E(-2,3)
H(3,3)
EH=sqrt%28%28x-x%5B1%5D%29%5E2%2B%28y-y%5B1%5D%29%5E2%29
EH=sqrt%28%283-%28-2%29%29%5E2%2B%283-3%29%5E2%29
EH=sqrt%28%283%2B2%29%5E2%2B0%5E2%29
EH=sqrt%285%5E2%29
highlight%28EH=5%29
as you can see, all sides are same length which proves that a quadrilateral is a rhombus