Study Guides/Maths/Diagonals of a Rhombus
Study Guide · Maths

Properties of the Diagonals of a Rhombus

A Rhombus is a special type of parallelogram where all four sides are equal in length (like a slanted square). While its sides are equal, its most unique and tested geometric properties lie in its diagonals.

Question (Click to Flip)

Do the diagonals of a rhombus bisect each other at 90 degrees?

Answer

Yes, the diagonals of a rhombus are perpendicular bisectors, meaning they cut each other exactly in half and meet at exactly 90 degrees.

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Key Facts

Diagonals Bisect each other (cut in half).

Diagonals are Perpendicular (meet at 90°).

Diagonals Bisect vertex angles.

Area = ½ × (diagonal 1 × diagonal 2).

Important: The diagonals of a rhombus are NOT equal in length (unless it is a perfect square).

The 3 Golden Properties of Rhombus Diagonals

1. They bisect each other Like all parallelograms, the two diagonals of a rhombus cut each other exactly in half. If diagonal PR is 10cm, the intersection point cuts it into 5cm and 5cm.

2. They intersect at exactly 90 degrees (Right Angles) This is the most famous property. The diagonals are perpendicular bisectors of each other. The point where they cross forms four perfect 90° right angles inside the rhombus. (Because of this, you can use Pythagoras Theorem on the four inner triangles!)

3. They bisect the opposite angles When a diagonal is drawn from one corner to the opposite corner, it cuts the corner angle into two exactly equal halves.

Area Formula Using Diagonals

Because the diagonals intersect at 90 degrees, finding the area of a rhombus is very easy if you know the lengths of the two diagonals (let's call them d₁ and d₂).

Area = ½ × (d₁ × d₂)

Questions and Answers

Do the diagonals of a rhombus bisect each other at 90 degrees?+

Yes, the diagonals of a rhombus are perpendicular bisectors, meaning they cut each other exactly in half and meet at exactly 90 degrees.

Are the diagonals of a rhombus equal in length?+

No, in a standard rhombus, one diagonal is longer than the other. They are only equal if the rhombus has 90-degree corners, which would make it a square.

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