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Home Vectors Vectors and Plane Geometry Examples Example 7: Diagonals of a Parallelogram Bisect Each Other
 
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Example 7: Diagonals of a Parallelogram Bisect Each Other (Proof)

Prove that the diagonals of a parallelogram bisect each other.

PROOF

We are given a parallelogram ABCD, shown in Figure 10.2.13.

Since the opposite sides represent equal vectors, we have

(2) B - A = C - D.

The diagonal AC has midpoint ½A + ½C and the other diagonal BD has midpoint ½B + ½D. We show that these two midpoints are equal. The Equation 2 gives

C = B - A + D.

Then

½A + ½C = ½A + ½(B - A + D) = ½B + ½D.

Thus the two diagonals meet at their midpoints.
Home Vectors Vectors and Plane Geometry Examples Example 7: Diagonals of a Parallelogram Bisect Each Other

Last Update: 2006-11-15