Parallelograms have congruent and parallel opposite sides.
The correct statement is: (a) find the slopes of pairs of opposite sides to show that the figure is a parallelogram.
The given parameters are:
[tex]\mathbf{A = (6,1)}[/tex]
[tex]\mathbf{B = (8,2)}[/tex]
[tex]\mathbf{C = (9,4)}[/tex]
[tex]\mathbf{D = (7,3)}[/tex]
To prove the type of quadrilateral, the shape is; the slopes of opposite sides must be calculated.
The parallel sides are: AB and CD
The slopes are calculated using:
[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]
So, we have:
[tex]\mathbf{m_{AB} = \frac{2 - 1}{8 - 6}}[/tex]
[tex]\mathbf{m_{AB} = \frac{1}{2}}[/tex]
[tex]\mathbf{m_{AB} = 0.5}[/tex]
[tex]\mathbf{m_{CD} = \frac{3 - 4}{7 - 9}}[/tex]
[tex]\mathbf{m_{CD} = \frac{- 1}{- 2}}[/tex]
[tex]\mathbf{m_{CD} = 0.5}[/tex]
Hence, the correct statement is: (a) find the slopes of pairs of opposite sides to show that the figure is a parallelogram.
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