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Q1. If a quadrilateral has two pairs of opposite sides that are equal, what can be concluded about the quadrilateral?
Solution:
A quadrilateral with two pairs of opposite sides that are equal is a parallelogram by definition.
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Q2. In a trapezoid, if the lengths of the bases are 10 cm and 6 cm, what is the length of the midsegment?
Solution:
The length of the midsegment of a trapezoid is the average of the lengths of the bases: (10 cm + 6 cm) / 2 = 8 cm.
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Q3. In a rhombus, if one angle measures 60 degrees, what is the measure of the adjacent angle?
Solution:
In a rhombus, adjacent angles are supplementary. Therefore, if one angle is 60 degrees, the adjacent angle is 180 - 60 = 120 degrees.
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Q4. If a quadrilateral is a rectangle, what can be said about its diagonals?
Solution:
In a rectangle, the diagonals are equal in length and bisect each other.
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Q5. If a quadrilateral is a kite, what can be said about its diagonals?
Solution:
In a kite, one diagonal bisects the other diagonal.
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Q6. In a trapezoid, if the lengths of the bases are 10 cm and 6 cm, what is the average length of the bases?
Solution:
The average length of the bases is calculated as (10 cm + 6 cm) / 2 = 8 cm.
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