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isosceles trapezoid abcd is shown below with a line ef drawn through its center. if the isosceles trapezoid is dilated using a scale factor of one half and a line is drawn through the center of the new dilated figure, what relationship will that line have with line ef in the drawing below

The new line is parallel to EF or we can say that the line E'F' is same as the line EF but the length of line E'F' is half of the length of EF.

An isosceles trapezoid is characterized by its symmetry. The line EF, divides in two equal parts the trapezoid, if we divide again the trapezoid with the line E'F', we well have four equal part, and the new line would be parallel to EF.

Also, due to the symmetry, the new line will be proportional to EF. The problem says that E'F' would have the scale factor of one half, this means that the new line will be half EF, because its factor divides by two.

Remember that all this proportionality is based on Thales' theorem, which says that if we have two transversal crossing parallels, we would have proportional sides, and each portion of parallels would be proportional too.

Therefore, the new line would be half of EF and parallel to it.

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