Answer :

The relationship between the slopes of the parallel sides is m₁ = m₂.

The relationship between the lengths of the non-parallel sides is perpendicular or intersecting.

How to find the slope of a line?

The slope of a line can be calculated by taking the tangent ratio of the angle formed by it with the x axis.

The angle between two parallel lines is zero.

This implies that they form same angle with the x-axis.

The slopes of two parallel lines are always equal to each other.

Since, the slope of a line is the tangent of the angle made by it with x axis.

Then, it can be written as m₁ = m₂.

Hence, the relationship between the lengths of the non-parallel sides;

perpendicular or intersecting.

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mhanifa

Answer:

  • The slopes are equal;
  • The non-parallel sides are congruent (equal)

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The slopes of the parallel sides are equal. We can prove this by finding the slopes:

  • [tex]m(DG) = (2 - 2)/(1 - (-2)) = 0/3 = 0[/tex]
  • [tex]m(EF) = (- 3 - (-3))/(3 - (-3)) = 0/7 = 0[/tex]
  • The slopes are equal

We can see the non-parallel sides have same length. Let us  prove this by finding their length:

  • [tex]ED=\sqrt{(-4+2)^2+(-3-2)^2} =\sqrt{4+25} =\sqrt{29}[/tex]
  • [tex]FG=\sqrt{(1-3)^2+(2-(-3))^2} =\sqrt{4+25} =\sqrt{29}[/tex]
  • The sides are equal

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