Diagonals of a Rectangle

Diagonals of a Rectangle

How to solve the diagonals of a rectangle problems: property, example, and its solution.

Property

The segments formed by bisecting diagonals of a rectangle are all congruent.

The segments
formed by bisecting diagonals of a rectangle
are all congruent.

Recall that the segments
formed by diagonals of a parallelogram
are not all congruent:
segments from different diagonals are not congruent.

Example

Find the value of x. The segment formed by bisecting diagonals: 5. Sides: x, 6.

The blue segments are all congruent: 5.

See the right triangle
whose base is the brown side.

Its hypotenuse is 10. (= 5 + 5)
And its legs are 6 and x.

So this is similar to a (3, 4, 5) triangle.

Draw a (3, 4, 5) triangle next to the right triangle.

The left triangle is × 2 bigger.

So x = 2⋅4.