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.