Question

GeometryQuestion 5•For what values of the variables must ABCD be a parallelogram?

Answer 1

SOLUTION:

For parallelograms; opposite sides are congruent;

Thus;

$\begin{gathered} 2y-12=y-2 \\ solving\text{ for y} \\ 2y-y=12-2 \\ y=10 \end{gathered}$

The shorter opposite sides must be equal too, thus;

$\begin{gathered} 2x+1=y+3 \\ substitute\text{ in y = 10} \\ 2x+1=10+3 \\ 2x+1=13 \\ 2x=12 \\ x=6 \end{gathered}$

Thus, for the figure to be a parallelogram, x = 6 and y = 10