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Explain how to use the midpoint formula to prove or disapprove that ABCD is a parallelogram

Explain how to use the midpoint formula to prove or disapprove that ABCD is a parallelogram-example-1
User RONE
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1 Answer

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20 votes

Step 1

The property of a parallelogram is that diagonals of a parallelogram bisect each other and hence have the same midpoint.

This means that the diagonals cut themselves into two equal halves.

Hence, they must have the same mid-points.

Therefore, if we prove that AC and BD have the same midpoint, then ABCD is a parallelogram.

Step 2

Find the midpoint of BD and AC


\begin{gathered} ((x_2+x_1)/(2)),((y_2+y_1)/(2)) \\ BD=(-(1)/(2),(9)/(2)) \\ AC=(-(1)/(2),(9)/(2)) \end{gathered}

Since they have the same midpoint, the answer will be;

We Prove that AC and BD have the same midpoint which we have done. we know the diagonals of a parallelogram bisect each other; therefore, they have the same midpoint and ABCD is a parallelogram.

User ChoiZ
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