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41. Write a proof of the theorem that states if an angle of a quadrilateral is supplementary to both of its consecutive angles, the quadrilateral is a parallelogram.
Given: m∠F + m∠G = 180, m∠F + m∠J = 180
Prove: FGHJ is a parallelogram
What statement proves the theorem?
A. By the Angle Addition Postulate m∠F = m∠J and m∠G = m∠H. So, by the definition of a parallelogram, FGHJ is a parallelogram.
B. By the Converse of the Same-Side Interior Angles Postulate, FJ|| GHand FG||JH. So, by the definition of a parallelogram, FGHJ is a parallelogram.
C. By the Polygon Interior Angle-Sum Theorem, m∠F + m∠G + m∠F + m∠J = 360. So, by the definition of a parallelogram, FGHJ is a parallelogram.
D. By the Converse of the Same-Side Interior Angles Postulate, FJ = JH andFG=JH. So, by the definition of a parallelogram, FGHJ is a parallelogram.
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