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Answer :
A trapezoid is defined as a quadrilateral with one pair of parallel sides. In the quadrilateral [tex]\(JKLM\)[/tex], the sides are usually listed in order. This means the pair of sides that are opposite each other are [tex]\(JK\)[/tex] and [tex]\(LM\)[/tex]. Therefore, it must be true that
[tex]$$
JK \parallel LM.
$$[/tex]
Let’s review the options:
1. Option A states [tex]\(JK = IM\)[/tex]. There is no requirement in the definition of a trapezoid for any pair of sides to be congruent (equal in length).
2. Option B states [tex]\(JK \parallel LM\)[/tex]. Since a trapezoid must have exactly one pair of parallel sides, this condition must be true.
3. Option C states that [tex]\(\angle J\)[/tex] is supplementary to [tex]\(\angle K\)[/tex]. There is no inherent relationship that forces these angles to be supplementary in every trapezoid.
4. Option D claims that [tex]\(KL \parallel JM\)[/tex]. This is not necessarily true for a generic trapezoid, as only one pair of opposite sides must be parallel.
5. Option E states that [tex]\(\angle J\)[/tex] is congruent to [tex]\(\angle K\)[/tex]. There is no requirement in a trapezoid for any two angles to be equal unless additional information (like it being an isosceles trapezoid) is provided.
Thus, the only statement that must be true is Option B.
The final answer is that only Option B is correct.
[tex]$$
JK \parallel LM.
$$[/tex]
Let’s review the options:
1. Option A states [tex]\(JK = IM\)[/tex]. There is no requirement in the definition of a trapezoid for any pair of sides to be congruent (equal in length).
2. Option B states [tex]\(JK \parallel LM\)[/tex]. Since a trapezoid must have exactly one pair of parallel sides, this condition must be true.
3. Option C states that [tex]\(\angle J\)[/tex] is supplementary to [tex]\(\angle K\)[/tex]. There is no inherent relationship that forces these angles to be supplementary in every trapezoid.
4. Option D claims that [tex]\(KL \parallel JM\)[/tex]. This is not necessarily true for a generic trapezoid, as only one pair of opposite sides must be parallel.
5. Option E states that [tex]\(\angle J\)[/tex] is congruent to [tex]\(\angle K\)[/tex]. There is no requirement in a trapezoid for any two angles to be equal unless additional information (like it being an isosceles trapezoid) is provided.
Thus, the only statement that must be true is Option B.
The final answer is that only Option B is correct.
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