# Geometry Problem 1520: Discovering Distances in a Rectangle with an Exterior Point: A Geometry Challenge. Difficulty Level: High School.

In a rectangle ABCD, E is an exterior point such that AC and DE measure 24 units each, and angles CAD and CDE are congruent. Calculate BE. See the figure or diagram below.

## Definitions and Suggestions

Theorem Description
Rectangle In a rectangle, opposite sides are congruent and parallel.
The diagonals of a rectangle are congruent.
The diagonals of a rectangle bisect each other.
Congruent Angles Congruent angles are angles that have the same measure.
45-45-90 Triangle A 45-45-90 triangle is a right triangle with two legs that are congruent and a hypotenuse that is √2 times the length of a leg.

### Thematic Poem: Journey of Geometry: Discovering Distances in a Rectangle with an Exterior Point

Discovering distances in a rectangle so fair,
With an exterior point beyond compare,
Geometry challenges waiting to be found,
A journey of discovery, unbound.

Congruent segments beckon with delight,
Angles matching in a perfect sight,
BD and DE measure 24 each,
A puzzle to solve, within our reach.

CAD and CDE congruent and true,
A fascinating problem for me and you,
Together we will find the length of BE,
A journey of learning, for us to see.

So let us embark on this geometry quest,
A challenge so great, we won't rest,
Discovering distances, angles, and more,
In a rectangle, with an exterior point to explore.

If you're interested in finding more poems with a focus on geometry, you may enjoy this collection: More geometry thematic poems.