Question

MANE is a quadrilateral with vertices M (6,20), A(10,8), N(4,0) and E (0,12).

Answer 1

To prove that MANE is a parallelogram, you need to show that opposite sides are parallel.  Use the slope formula to show that opposite sides have the same slope.

$Slope\ (m)\ of\ \overline{ME} = \dfrac{20-12}{6-0}=\dfrac{8}{6}=\dfrac{4}{3}\\\\\\Slope\ (m)\ of\ \overline{AN} = \dfrac{8-0}{10-4}=\dfrac{8}{6}=\dfrac{4}{3}\\\\\\\overline{ME}\ ||\ \overline{AN}\\\\Slope\ (m)\ of\ \overline{MA} = \dfrac{20-8}{6-10}=\dfrac{12}{-4}=-3\\\\\\Slope\ (m)\ of\ \overline{EN} = \dfrac{12-0}{0-4}=\dfrac{12}{-4}=-3\\\\\\\overline{MA}\ ||\ \overline{EN}$