Showing that the legs of trapezoid CDEF are non-parallel (they have different slopes) and are congruent (they have the same length), we can prove that it is an isosceles trapezoid.
An isosceles trapezoid can be described as trapezoid whose non-parallel sides or legs are congruent to each other, that is, they have equal lengths.
Two segments can only be considered parallel to each other only if they have the same slope.
Given that CDEF is a trapezoid, to prove that it is an isosceles trapezoid, we have to find the slope of the two legs and also their lengths.
Given:
C(0, 2), D(2, 4), E(7, 3), and F(1, –3)
Find slopes of CF and DE:
Slope of CF = change in y/change in x = (2 -(-3))/(0 - 1) = 5/-1 = -5
Slope of DE = change in y/change in x = (4 - 3)/(2 - 7) = 1/-5 = -1/5
The legs of the trapezoid, CF and DE have different slopes.
Using the distance formula, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], the lengths of the legs are:
CF = √26
DE = √26
Since the legs of trapezoid CDEF have the same length and different slopes (non-parallel), therefore, we can prove that it is an isosceles trapezoid.
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