Question 121766
Rectangles are parallelograms, you can check their definitions.

For example, graph and label the following points: 

A({{{ -9}}},{{{ -2}}}); 

B({{{ -7}}},{{{2}}});

C({{{ -4}}},{{{3}}});

D({{{ -6}}},{{{ -1}}}). 

and prove if the figure forms a {{{parallelogram}}}, using {{{slope=m}}} to do so:



find a slope of line that goes throug these two points:

A({{{ -9}}},{{{ -2}}}); D({{{ -6}}},{{{ -1}}}). 

{{{m[1] = ((y[2]-y[1])/(x[2]-x[1]))}}}

{{{m[1] = (-1-(-2))/(-6-(-9))}}}

{{{highlight(m[1] = 1/3)}}}


find a slope of line that goes throug these two points:

B({{{ -7}}},{{{2}}}); C({{{ -4}}},{{{3}}});


{{{m[2] = (y[2]-y[1])/(x[2]-x[1])}}}


{{{m[2] = (3 - 2)/(-4-(-7))}}}


{{{highlight(m[2] = 1/ 3)}}}……….


 => the figure does {{{form_ a_ parallelogram}}} because opposite sides {{{AD}}} and {{{BC}}} of figure {{{ABCD}}} are {{{parallel}}} to one another; they have the {{{same }}}{{{slope}}});

 {{{m[1] = m[2]}}}