Question

Find the midpoint of each side of the trapezoid. Connect the midpoints. What is the most precise classification of the quadrilateral formed by connecting the midpoints of the sides of the trapezoid?

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Answer 1

The midpoints of the sides of the trapezoid are:
M ( - 1 , 1 ), N ( 1, - 1 ), P ( 3, 1 ), Q ( 1, 3 ).
MN = NP = PQ = QM = √ ( 2² + 2² ) = √ 8 = 2√2
∠MNP = ∠NPQ = ∠PQM = ∠QMN = 90°
Answer:
The quadrilateral formed by joining the midpoints of the sides of the trapezoid is a square.