Diagonals of a rhombus are perpendicular.

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Multiple Choice

Diagonals of a rhombus are perpendicular.

In a rhombus, all sides are equal, so treat two adjacent sides as vectors a and b with the same length. The diagonals align with a + b and a − b. The angle between these diagonals is determined by their dot product: (a + b) · (a − b) = |a|^2 − |b|^2. Since |a| = |b|, this becomes zero, meaning the diagonals meet at a right angle. So, diagonals in every rhombus are perpendicular.

In a rhombus, all sides are equal, so treat two adjacent sides as vectors a and b with the same length. The diagonals align with a + b and a − b. The angle between these diagonals is determined by their dot product: (a + b) · (a − b) = |a|^2 − |b|^2. Since |a| = |b|, this becomes zero, meaning the diagonals meet at a right angle. So, diagonals in every rhombus are perpendicular.

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