Question 1137036

A({{{5}}},{{{7}}})  B({{{15}}},{{{3}}})  C({{{13}}},{{{-2}}}),  D({{{3}}},{{{2}}})


{{{drawing ( 600, 600, -5, 20, -5, 20,
circle(5,7,.12),locate(5,7,A(5,7)),
circle(15,3,.12),locate(15,3,B(15,3)),
circle(13,-2,.12),locate(13,-2,C(13,-2)),
circle(3,2,.12),locate(3,2,D(3,2)),
line(5,7,15,3),line(5,7,3,2),line(13,-2,15,3),line(13,-2,3,2),
line(5,7,13,-2),line(15,3,3,2),
graph( 600, 600, -5, 20, -5, 20, 0)) }}}


now use distance formula and prove that the distance {{{AC=BD}}}

{{{AC=sqrt((13-5)^2+(-2-7)^2)}}}

{{{AC=sqrt(8^2+(-9)^2)}}}

{{{AC=sqrt(64+81)}}}

{{{AC=sqrt(145)}}}

{{{AC=12.0415945787923}}}


{{{BD=sqrt((15-3)^2+(3-2)^2)}}}

{{{BD=sqrt(12^2+1^2)}}}

{{{BD=sqrt(144+1)}}}

{{{BD=sqrt(145)}}}

{{{BD=12.0415945787923}}}


=>the diagonals are congruent