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Given ef is the midsegment of isosceles trapezoid abcd bc equals 17x ef equals 22.5x plus 9 and ad equals 30x plus 12 find ad?

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Q: Given ef is the midsegment of isosceles trapezoid abcd bc equals 17x ef equals 22.5x plus 9 and ad equals 30x plus 12 find ad?

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It is an isosceles trapezoid that fits the given description.

An isosceles trapezoid would fit the given description.

With the information given it can be any height greater than zero units. If the area was given, or the lengths of the equal sides were given, then the height can be calculated specifically.

No, never. A trapezoid may have diagonals of equal length (isosceles trapezoid), but they do not intersect at their midpoints.Draw the diagonals of a trapezoid, for example, an isosceles trapezoid, thereby creating 4 triangles inside the trapezoid. Now assume the diagonals do bisect each other. The congruent corresponding sides of the top and bottom triangles with the included vertical angle would make the triangles congruent by the side-angle-side theorem. But this is a contradiction since the respective bases of the triangles, forming the top and bottom of the trapezoid are, of course, not equal. Therefore, the triangles cannot be congruent. Hence, we have given proof by contradiction that diagonals in a trapezoid cannot bisect each other.

The dimensions given are not that of a rectangle but are probably that of an isosceles trapezoid in which case it is:- Area = 0.5*(8+10)*2 = 18 square feet

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The length of a midsegment is half that of the parallel side of the triangle; assuming the midsegment is parallel to the [given] base, then its length is 27 ÷ 2 = 13.5 units.

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