In a parallelogram, diagonals bisect each other.

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Multiple Choice

In a parallelogram, diagonals bisect each other.

In a parallelogram, the diagonals cross at their midpoints. This means the intersection point splits each diagonal into two equal parts. A quick way to see why is to use coordinates. Place A at (0,0), B at (x1,y1), and D at (x2,y2). Then C is at B + D = (x1+x2, y1+y2). The diagonal AC goes from (0,0) to (x1+x2, y1+y2), so its midpoint is ((x1+x2)/2, (y1+y2)/2). The diagonal BD goes from (x1,y1) to (x2,y2), and its midpoint is ((x1+x2)/2, (y1+y2)/2) as well. Since both diagonals share the same midpoint, each is bisected by the other. That’s why the statement is always true for any parallelogram. It’s not limited to rectangles, and it’s not “sometimes true.” The diagonals always bisect each other.

In a parallelogram, the diagonals cross at their midpoints. This means the intersection point splits each diagonal into two equal parts.

A quick way to see why is to use coordinates. Place A at (0,0), B at (x1,y1), and D at (x2,y2). Then C is at B + D = (x1+x2, y1+y2). The diagonal AC goes from (0,0) to (x1+x2, y1+y2), so its midpoint is ((x1+x2)/2, (y1+y2)/2). The diagonal BD goes from (x1,y1) to (x2,y2), and its midpoint is ((x1+x2)/2, (y1+y2)/2) as well. Since both diagonals share the same midpoint, each is bisected by the other.

That’s why the statement is always true for any parallelogram. It’s not limited to rectangles, and it’s not “sometimes true.” The diagonals always bisect each other.

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