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Zorluk: OrtaProperties of Quadrilaterals

In any trapezoid, the length of the midsegment connecting the midpoints of the non-parallel legs is equal to half the difference of the lengths of the two parallel bases.

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False. The length of the midsegment of a trapezoid is equal to half the sum of the lengths of the parallel bases, not half the difference.
The statement is false because the Trapezoid Midsegment Theorem dictates that the length of the midsegment connecting the midpoints of the non-parallel legs is equal to half the sum (the average) of the lengths of the parallel bases, b1+b22\frac{b_1 + b_2}{2}. Half the difference of the base lengths gives the length of the segment connecting the midpoints of the diagonals.

Adım Adım Çözüm

1
Recall the definition of a trapezoid midsegment.
The midsegment of a trapezoid is the line segment joining the midpoints of its non-parallel legs.
Identifying the geometric figure and segment being described is necessary to apply the correct theorem.
2
Apply the Trapezoid Midsegment Theorem.
The length mm of the midsegment for a trapezoid with parallel bases b1b_1 and b2b_2 is given by m=b1+b22m = \frac{b_1 + b_2}{2}.
The theorem states that the midsegment length is the average (half the sum) of the two base lengths.
3
Compare the theorem formula to the given statement.
The statement claims the length is ∣b1−b2∣2\frac{|b_1 - b_2|}{2} (half the difference), which contradicts the true formula b1+b22\frac{b_1 + b_2}{2}. Therefore, the statement is false.
Evaluating the mathematical validity of the statement determines the correct answer.

Anahtar Kavram

Trapezoid Midsegment Theorem
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Konular

Properties of Quadrilaterals

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