A trapezoid is in the shape of a stage. write a coordinate proof to prove that TR and SF are para

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What do "TR and SF" signify?

"para-"llel ?

To prove that TR and SF are parallel lines, we can use the concept of slope in a coordinate proof.

Let's assume that the trapezoid is located in a coordinate plane, and we have the coordinates of the points T, R, S, and F.

Point T can be represented as (x₁, y₁), R as (x₂, y₂), S as (x₃, y₃), and F as (x₄, y₄).

To prove that TR and SF are parallel, we need to show that the slopes of both lines are equal.

The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) can be found using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

For TR, the slope can be calculated as:

m₁ = (y₂ - y₁) / (x₂ - x₁)

Similarly, for SF, the slope can be calculated as:

m₂ = (y₄ - y₃) / (x₄ - x₃)

To prove that TR and SF are parallel, we need to prove that m₁ = m₂.

Therefore, compute the slopes m₁ and m₂ using the given coordinates of the points T, R, S, and F, and see if they are equal. If the slopes are equal, it implies that the lines TR and SF are parallel.